LMFDB - Embedded newform 546.2.k.c.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(373,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$-0.571299 + 1.29368i$ of defining polynomial
Character	$\chi$	$=$	546.373
Dual form			546.2.k.c.445.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.441221 + 0.764218i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.45374 - 0.989520i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.441221 + 0.764218i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.45374 - 0.989520i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.882443 q^{10} +1.55187 q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.13422 - 2.90605i) q^{13} +(0.369922 + 2.61976i) q^{14} +(-0.441221 + 0.764218i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.58796 - 6.21453i) q^{17} +(-0.500000 - 0.866025i) q^{18} +4.74161 q^{19} +(-0.441221 - 0.764218i) q^{20} +(-2.45374 - 0.989520i) q^{21} +(-0.775934 - 1.34396i) q^{22} +(-2.64674 - 4.58428i) q^{23} +1.00000 q^{24} +(2.11065 + 3.65575i) q^{25} +(-3.58382 - 0.395262i) q^{26} +1.00000 q^{27} +(2.08382 - 1.63024i) q^{28} +(3.87494 - 6.71160i) q^{29} +0.882443 q^{30} +(3.24911 + 5.62762i) q^{31} +(-0.500000 + 0.866025i) q^{32} +1.55187 q^{33} -7.17592 q^{34} +(1.83885 - 1.43860i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.165287 - 0.286285i) q^{37} +(-2.37080 - 4.10635i) q^{38} +(2.13422 - 2.90605i) q^{39} +(-0.441221 + 0.764218i) q^{40} +(-3.02918 + 5.24669i) q^{41} +(0.369922 + 2.61976i) q^{42} +(3.35975 + 5.81927i) q^{43} +(-0.775934 + 1.34396i) q^{44} +(-0.441221 + 0.764218i) q^{45} +(-2.64674 + 4.58428i) q^{46} +(0.976430 - 1.69123i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(5.04170 + 4.85605i) q^{49} +(2.11065 - 3.65575i) q^{50} +(3.58796 - 6.21453i) q^{51} +(1.44960 + 3.30131i) q^{52} +(-6.74308 - 11.6794i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.684718 + 1.18597i) q^{55} +(-2.45374 - 0.989520i) q^{56} +4.74161 q^{57} -7.74989 q^{58} +(-2.63569 + 4.56515i) q^{59} +(-0.441221 - 0.764218i) q^{60} -14.3518 q^{61} +(3.24911 - 5.62762i) q^{62} +(-2.45374 - 0.989520i) q^{63} +1.00000 q^{64} +(1.27919 + 2.91322i) q^{65} +(-0.775934 - 1.34396i) q^{66} -7.50473 q^{67} +(3.58796 + 6.21453i) q^{68} +(-2.64674 - 4.58428i) q^{69} +(-2.16529 - 0.873194i) q^{70} +(5.00985 + 8.67732i) q^{71} +1.00000 q^{72} +(-1.93284 - 3.34778i) q^{73} +(-0.165287 + 0.286285i) q^{74} +(2.11065 + 3.65575i) q^{75} +(-2.37080 + 4.10635i) q^{76} +(-3.80789 - 1.53560i) q^{77} +(-3.58382 - 0.395262i) q^{78} +(6.67928 - 11.5689i) q^{79} +0.882443 q^{80} +1.00000 q^{81} +6.05836 q^{82} -10.5519 q^{83} +(2.08382 - 1.63024i) q^{84} +(3.16617 + 5.48396i) q^{85} +(3.35975 - 5.81927i) q^{86} +(3.87494 - 6.71160i) q^{87} +1.55187 q^{88} +(-7.40837 - 12.8317i) q^{89} +0.882443 q^{90} +(-8.11241 + 5.01884i) q^{91} +5.29348 q^{92} +(3.24911 + 5.62762i) q^{93} -1.95286 q^{94} +(-2.09210 + 3.62362i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(5.79259 + 10.0331i) q^{97} +(1.68461 - 6.79427i) q^{98} +1.55187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 2 q^{5} - 4 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 2 * q^5 - 4 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 2 q^{5} - 4 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} + 4 q^{23} + 8 q^{24} + 2 q^{25} - 12 q^{26} + 8 q^{27} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 4 q^{32} - 8 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} - 6 q^{37} - 4 q^{38} + 3 q^{39} + 2 q^{40} + 12 q^{41} + 3 q^{42} + 4 q^{44} + 2 q^{45} + 4 q^{46} + 7 q^{47} - 4 q^{48} - 7 q^{49} + 2 q^{50} - 2 q^{51} + 9 q^{52} - q^{53} - 4 q^{54} - 25 q^{55} - 3 q^{56} + 8 q^{57} - 4 q^{58} + 16 q^{59} + 2 q^{60} + 8 q^{61} + 14 q^{62} - 3 q^{63} + 8 q^{64} + q^{65} + 4 q^{66} - 38 q^{67} - 2 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} + 8 q^{72} - 7 q^{73} - 6 q^{74} + 2 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} - 4 q^{80} + 8 q^{81} - 24 q^{82} - 64 q^{83} + 15 q^{85} + 2 q^{87} - 8 q^{88} - 11 q^{89} - 4 q^{90} - 20 q^{91} - 8 q^{92} + 14 q^{93} - 14 q^{94} + 28 q^{95} - 4 q^{96} + 11 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 2 * q^5 - 4 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 4 * q^10 - 8 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 + 2 * q^15 - 4 * q^16 - 2 * q^17 - 4 * q^18 + 8 * q^19 + 2 * q^20 - 3 * q^21 + 4 * q^22 + 4 * q^23 + 8 * q^24 + 2 * q^25 - 12 * q^26 + 8 * q^27 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 4 * q^32 - 8 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 - 6 * q^37 - 4 * q^38 + 3 * q^39 + 2 * q^40 + 12 * q^41 + 3 * q^42 + 4 * q^44 + 2 * q^45 + 4 * q^46 + 7 * q^47 - 4 * q^48 - 7 * q^49 + 2 * q^50 - 2 * q^51 + 9 * q^52 - q^53 - 4 * q^54 - 25 * q^55 - 3 * q^56 + 8 * q^57 - 4 * q^58 + 16 * q^59 + 2 * q^60 + 8 * q^61 + 14 * q^62 - 3 * q^63 + 8 * q^64 + q^65 + 4 * q^66 - 38 * q^67 - 2 * q^68 + 4 * q^69 - 22 * q^70 + 20 * q^71 + 8 * q^72 - 7 * q^73 - 6 * q^74 + 2 * q^75 - 4 * q^76 - 24 * q^77 - 12 * q^78 + 24 * q^79 - 4 * q^80 + 8 * q^81 - 24 * q^82 - 64 * q^83 + 15 * q^85 + 2 * q^87 - 8 * q^88 - 11 * q^89 - 4 * q^90 - 20 * q^91 - 8 * q^92 + 14 * q^93 - 14 * q^94 + 28 * q^95 - 4 * q^96 + 11 * q^97 + 2 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.441221	+	0.764218i	−0.197320	+	0.341769i	−0.947659	−	0.319285i	$-0.896557\pi$
$5$	−0.441221	+	0.764218i	−0.197320	+	0.341769i	0.750338	+	0.661054i	$0.229891\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−2.45374	−	0.989520i	−0.927427	−	0.374003i
$7$	−2.45374	−	0.989520i	−0.927427	−	0.374003i
$8$	1.00000			0.353553
$9$	1.00000			0.333333
$10$	0.882443			0.279053
$11$	1.55187			0.467906			0.233953	−	0.972248i	$-0.424834\pi$
$11$	1.55187			0.467906			0.233953	+	0.972248i	$0.424834\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	2.13422	−	2.90605i	0.591925	−	0.805993i
$13$	2.13422	−	2.90605i	0.591925	−	0.805993i
$14$	0.369922	+	2.61976i	0.0988658	+	0.700161i
$15$	−0.441221	+	0.764218i	−0.113923	+	0.197320i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.58796	−	6.21453i	0.870208	−	1.50724i	0.00842662	−	0.999964i	$-0.497318\pi$
$17$	3.58796	−	6.21453i	0.870208	−	1.50724i	0.861781	−	0.507280i	$-0.169349\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	4.74161			1.08780			0.543900	−	0.839150i	$-0.316947\pi$
$19$	4.74161			1.08780			0.543900	+	0.839150i	$0.316947\pi$
$20$	−0.441221	−	0.764218i	−0.0986601	−	0.170884i
$21$	−2.45374	−	0.989520i	−0.535450	−	0.215931i
$22$	−0.775934	−	1.34396i	−0.165430	−	0.286533i
$23$	−2.64674	−	4.58428i	−0.551883	−	0.955889i	−0.998139	−	0.0609839i	$-0.980576\pi$
$23$	−2.64674	−	4.58428i	−0.551883	−	0.955889i	0.446256	−	0.894905i	$-0.352757\pi$
$24$	1.00000			0.204124
$25$	2.11065	+	3.65575i	0.422129	+	0.731150i
$26$	−3.58382	−	0.395262i	−0.702845	−	0.0775173i
$27$	1.00000			0.192450
$28$	2.08382	−	1.63024i	0.393805	−	0.308087i
$29$	3.87494	−	6.71160i	0.719559	−	1.24631i	−0.241616	−	0.970372i	$-0.577677\pi$
$29$	3.87494	−	6.71160i	0.719559	−	1.24631i	0.961175	−	0.275940i	$-0.0889893\pi$
$30$	0.882443			0.161111
$31$	3.24911	+	5.62762i	0.583557	+	1.01075i	0.995054	+	0.0993390i	$0.0316728\pi$
$31$	3.24911	+	5.62762i	0.583557	+	1.01075i	−0.411497	+	0.911411i	$0.634994\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.55187			0.270146
$34$	−7.17592			−1.23066
$35$	1.83885	−	1.43860i	0.310823	−	0.243167i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−0.165287	−	0.286285i	−0.0271730	−	0.0470650i	0.852119	−	0.523348i	$-0.175317\pi$
$37$	−0.165287	−	0.286285i	−0.0271730	−	0.0470650i	−0.879292	+	0.476283i	$0.841984\pi$
$38$	−2.37080	−	4.10635i	−0.384595	−	0.666138i
$39$	2.13422	−	2.90605i	0.341748	−	0.465340i
$40$	−0.441221	+	0.764218i	−0.0697632	+	0.120833i
$41$	−3.02918	+	5.24669i	−0.473079	+	0.819396i	−0.999525	−	0.0308121i	$-0.990191\pi$
$41$	−3.02918	+	5.24669i	−0.473079	+	0.819396i	0.526447	+	0.850208i	$0.323524\pi$
$42$	0.369922	+	2.61976i	0.0570802	+	0.404238i
$43$	3.35975	+	5.81927i	0.512358	+	0.887430i	0.999897	+	0.0143288i	$0.00456116\pi$
$43$	3.35975	+	5.81927i	0.512358	+	0.887430i	−0.487540	+	0.873101i	$0.662106\pi$
$44$	−0.775934	+	1.34396i	−0.116977	+	0.202609i
$45$	−0.441221	+	0.764218i	−0.0657734	+	0.113923i
$46$	−2.64674	+	4.58428i	−0.390240	+	0.675916i
$47$	0.976430	−	1.69123i	0.142427	−	0.246691i	−0.785983	−	0.618248i	$-0.787843\pi$
$47$	0.976430	−	1.69123i	0.142427	−	0.246691i	0.928410	+	0.371557i	$0.121176\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	5.04170	+	4.85605i	0.720243	+	0.693722i
$50$	2.11065	−	3.65575i	0.298491	−	0.517001i
$51$	3.58796	−	6.21453i	0.502415	−	0.870208i
$52$	1.44960	+	3.30131i	0.201024	+	0.457809i
$53$	−6.74308	−	11.6794i	−0.926233	−	1.60428i	−0.789566	−	0.613666i	$-0.789694\pi$
$53$	−6.74308	−	11.6794i	−0.926233	−	1.60428i	−0.136667	−	0.990617i	$-0.543639\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−0.684718	+	1.18597i	−0.0923273	+	0.159916i
$56$	−2.45374	−	0.989520i	−0.327895	−	0.132230i
$57$	4.74161			0.628041
$58$	−7.74989			−1.01761
$59$	−2.63569	+	4.56515i	−0.343137	+	0.594332i	−0.985014	−	0.172477i	$-0.944823\pi$
$59$	−2.63569	+	4.56515i	−0.343137	+	0.594332i	0.641876	+	0.766808i	$0.278156\pi$
$60$	−0.441221	−	0.764218i	−0.0569614	−	0.0986601i
$61$	−14.3518			−1.83756			−0.918782	−	0.394765i	$-0.870826\pi$
$61$	−14.3518			−1.83756			−0.918782	+	0.394765i	$0.870826\pi$
$62$	3.24911	−	5.62762i	0.412637	−	0.714708i
$63$	−2.45374	−	0.989520i	−0.309142	−	0.124668i
$64$	1.00000			0.125000
$65$	1.27919	+	2.91322i	0.158664	+	0.361340i
$66$	−0.775934	−	1.34396i	−0.0955109	−	0.165430i
$67$	−7.50473			−0.916849			−0.458424	−	0.888733i	$-0.651586\pi$
$67$	−7.50473			−0.916849			−0.458424	+	0.888733i	$0.651586\pi$
$68$	3.58796	+	6.21453i	0.435104	+	0.753622i
$69$	−2.64674	−	4.58428i	−0.318630	−	0.551883i
$70$	−2.16529	−	0.873194i	−0.258801	−	0.104367i
$71$	5.00985	+	8.67732i	0.594560	+	1.02981i	0.993609	+	0.112879i	$0.0360072\pi$
$71$	5.00985	+	8.67732i	0.594560	+	1.02981i	−0.399049	+	0.916930i	$0.630660\pi$
$72$	1.00000			0.117851
$73$	−1.93284	−	3.34778i	−0.226222	−	0.391828i	0.730464	−	0.682952i	$-0.239304\pi$
$73$	−1.93284	−	3.34778i	−0.226222	−	0.391828i	−0.956685	+	0.291124i	$0.905971\pi$
$74$	−0.165287	+	0.286285i	−0.0192142	+	0.0332800i
$75$	2.11065	+	3.65575i	0.243717	+	0.422129i
$76$	−2.37080	+	4.10635i	−0.271950	+	0.471031i
$77$	−3.80789	−	1.53560i	−0.433949	−	0.174998i
$78$	−3.58382	−	0.395262i	−0.405788	−	0.0447546i
$79$	6.67928	−	11.5689i	0.751478	−	1.30160i	−0.195629	−	0.980678i	$-0.562675\pi$
$79$	6.67928	−	11.5689i	0.751478	−	1.30160i	0.947106	−	0.320920i	$-0.103992\pi$
$80$	0.882443			0.0986601
$81$	1.00000			0.111111
$82$	6.05836			0.669034
$83$	−10.5519			−1.15822			−0.579109	−	0.815250i	$-0.696599\pi$
$83$	−10.5519			−1.15822			−0.579109	+	0.815250i	$0.696599\pi$
$84$	2.08382	−	1.63024i	0.227363	−	0.177874i
$85$	3.16617	+	5.48396i	0.343419	+	0.594820i
$86$	3.35975	−	5.81927i	0.362292	−	0.627508i
$87$	3.87494	−	6.71160i	0.415437	−	0.719559i
$88$	1.55187			0.165430
$89$	−7.40837	−	12.8317i	−0.785285	−	1.36015i	−0.928829	−	0.370510i	$-0.879183\pi$
$89$	−7.40837	−	12.8317i	−0.785285	−	1.36015i	0.143543	−	0.989644i	$-0.454150\pi$
$90$	0.882443			0.0930176
$91$	−8.11241	+	5.01884i	−0.850412	+	0.526118i
$92$	5.29348			0.551883
$93$	3.24911	+	5.62762i	0.336917	+	0.583557i
$94$	−1.95286			−0.201422
$95$	−2.09210	+	3.62362i	−0.214645	+	0.371776i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	5.79259	+	10.0331i	0.588149	+	1.01870i	0.994475	+	0.104975i	$0.0334764\pi$
$97$	5.79259	+	10.0331i	0.588149	+	1.01870i	−0.406326	+	0.913728i	$0.633190\pi$
$98$	1.68461	−	6.79427i	0.170172	−	0.686325i
$99$	1.55187			0.155969
$100$	−4.22129			−0.422129
$101$	7.82879			0.778994			0.389497	−	0.921028i	$-0.372649\pi$
$101$	7.82879			0.778994			0.389497	+	0.921028i	$0.372649\pi$
$102$	−7.17592			−0.710522
$103$	0.430172	−	0.745081i	0.0423862	−	0.0734150i	−0.844054	−	0.536258i	$-0.819837\pi$
$103$	0.430172	−	0.745081i	0.0423862	−	0.0734150i	0.886440	+	0.462843i	$0.153171\pi$
$104$	2.13422	−	2.90605i	0.209277	−	0.284961i
$105$	1.83885	−	1.43860i	0.179454	−	0.140393i
$106$	−6.74308	+	11.6794i	−0.654946	+	1.13440i
$107$	4.07130	+	7.05170i	0.393587	+	0.681713i	0.992920	−	0.118787i	$-0.0379005\pi$
$107$	4.07130	+	7.05170i	0.393587	+	0.681713i	−0.599332	+	0.800500i	$0.704567\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	4.73806	+	8.20656i	0.453824	+	0.786046i	0.998620	−	0.0525229i	$-0.0167263\pi$
$109$	4.73806	+	8.20656i	0.453824	+	0.786046i	−0.544796	+	0.838569i	$0.683393\pi$
$110$	1.36944			0.130571
$111$	−0.165287	−	0.286285i	−0.0156883	−	0.0271730i
$112$	0.369922	+	2.61976i	0.0349543	+	0.247544i
$113$	5.71537	+	9.89931i	0.537657	+	0.931249i	0.999030	+	0.0440426i	$0.0140237\pi$
$113$	5.71537	+	9.89931i	0.537657	+	0.931249i	−0.461373	+	0.887206i	$0.652643\pi$
$114$	−2.37080	−	4.10635i	−0.222046	−	0.384595i
$115$	4.67119			0.435591
$116$	3.87494	+	6.71160i	0.359779	+	0.623156i
$117$	2.13422	−	2.90605i	0.197308	−	0.268664i
$118$	5.27138			0.485270
$119$	−14.9533	+	11.6985i	−1.37077	+	1.07240i
$120$	−0.441221	+	0.764218i	−0.0402778	+	0.0697632i
$121$	−8.59170			−0.781064
$122$	7.17592	+	12.4291i	0.649677	+	1.12527i
$123$	−3.02918	+	5.24669i	−0.273132	+	0.473079i
$124$	−6.49821			−0.583557
$125$	−8.13726			−0.727819
$126$	0.369922	+	2.61976i	0.0329553	+	0.233387i
$127$	3.02592	−	5.24105i	0.268507	−	0.465068i	−0.699969	−	0.714173i	$-0.746803\pi$
$127$	3.02592	−	5.24105i	0.268507	−	0.465068i	0.968477	+	0.249105i	$0.0801363\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	3.35975	+	5.81927i	0.295810	+	0.512358i
$130$	1.88332	−	2.56442i	0.165178	−	0.224915i
$131$	−2.66045	+	4.60804i	−0.232445	+	0.402606i	−0.958527	−	0.285002i	$-0.908006\pi$
$131$	−2.66045	+	4.60804i	−0.232445	+	0.402606i	0.726082	+	0.687608i	$0.241339\pi$
$132$	−0.775934	+	1.34396i	−0.0675364	+	0.116977i
$133$	−11.6347	−	4.69191i	−1.00885	−	0.406841i
$134$	3.75236	+	6.49929i	0.324155	+	0.561453i
$135$	−0.441221	+	0.764218i	−0.0379743	+	0.0657734i
$136$	3.58796	−	6.21453i	0.307665	−	0.532891i
$137$	4.00561	−	6.93792i	0.342222	−	0.592747i	−0.642623	−	0.766183i	$-0.722154\pi$
$137$	4.00561	−	6.93792i	0.342222	−	0.592747i	0.984845	+	0.173436i	$0.0554870\pi$
$138$	−2.64674	+	4.58428i	−0.225305	+	0.390240i
$139$	8.87582	+	15.3734i	0.752838	+	1.30395i	0.946442	+	0.322873i	$0.104649\pi$
$139$	8.87582	+	15.3734i	0.752838	+	1.30395i	−0.193605	+	0.981080i	$0.562018\pi$
$140$	0.326435	+	2.31179i	0.0275888	+	0.195382i
$141$	0.976430	−	1.69123i	0.0822303	−	0.142427i
$142$	5.00985	−	8.67732i	0.420418	−	0.728185i
$143$	3.31202	−	4.50981i	0.276965	−	0.377129i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.41942	+	5.92260i	0.283967	+	0.491845i
$146$	−1.93284	+	3.34778i	−0.159963	+	0.277064i
$147$	5.04170	+	4.85605i	0.415833	+	0.400520i
$148$	0.330574			0.0271730
$149$	17.3232			1.41917			0.709587	−	0.704618i	$-0.248882\pi$
$149$	17.3232			1.41917			0.709587	+	0.704618i	$0.248882\pi$
$150$	2.11065	−	3.65575i	0.172334	−	0.298491i
$151$	−1.40927	−	2.44093i	−0.114685	−	0.198640i	0.802969	−	0.596021i	$-0.203252\pi$
$151$	−1.40927	−	2.44093i	−0.114685	−	0.198640i	−0.917654	+	0.397381i	$0.869919\pi$
$152$	4.74161			0.384595
$153$	3.58796	−	6.21453i	0.290069	−	0.502415i
$154$	0.574070	+	4.06553i	0.0462599	+	0.327610i
$155$	−5.73430			−0.460590
$156$	1.44960	+	3.30131i	0.116061	+	0.264316i
$157$	6.39822	+	11.0820i	0.510634	+	0.884443i	0.999924	+	0.0123225i	$0.00392247\pi$
$157$	6.39822	+	11.0820i	0.510634	+	0.884443i	−0.489290	+	0.872121i	$0.662744\pi$
$158$	−13.3586			−1.06275
$159$	−6.74308	−	11.6794i	−0.534761	−	0.926233i
$160$	−0.441221	−	0.764218i	−0.0348816	−	0.0604167i
$161$	1.95817	+	13.8677i	0.154326	+	1.09292i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−10.6877			−0.837129			−0.418564	−	0.908187i	$-0.637467\pi$
$163$	−10.6877			−0.837129			−0.418564	+	0.908187i	$0.637467\pi$
$164$	−3.02918	−	5.24669i	−0.236539	−	0.409698i
$165$	−0.684718	+	1.18597i	−0.0533052	+	0.0923273i
$166$	5.27593	+	9.13819i	0.409492	+	0.709261i
$167$	−9.90412	+	17.1544i	−0.766404	+	1.32745i	0.173097	+	0.984905i	$0.444623\pi$
$167$	−9.90412	+	17.1544i	−0.766404	+	1.32745i	−0.939501	+	0.342546i	$0.888711\pi$
$168$	−2.45374	−	0.989520i	−0.189310	−	0.0763431i
$169$	−3.89023	−	12.4043i	−0.299249	−	0.954175i
$170$	3.16617	−	5.48396i	0.242834	−	0.420601i
$171$	4.74161			0.362600
$172$	−6.71951			−0.512358
$173$	−1.73866			−0.132188			−0.0660941	−	0.997813i	$-0.521054\pi$
$173$	−1.73866			−0.132188			−0.0660941	+	0.997813i	$0.521054\pi$
$174$	−7.74989			−0.587517
$175$	−1.56155	−	11.0588i	−0.118042	−	0.835966i
$176$	−0.775934	−	1.34396i	−0.0584883	−	0.101305i
$177$	−2.63569	+	4.56515i	−0.198111	+	0.343137i
$178$	−7.40837	+	12.8317i	−0.555281	+	0.961774i
$179$	9.79287			0.731954			0.365977	−	0.930624i	$-0.380735\pi$
$179$	9.79287			0.731954			0.365977	+	0.930624i	$0.380735\pi$
$180$	−0.441221	−	0.764218i	−0.0328867	−	0.0569614i
$181$	−11.5901			−0.861486			−0.430743	−	0.902475i	$-0.641748\pi$
$181$	−11.5901			−0.861486			−0.430743	+	0.902475i	$0.641748\pi$
$182$	8.40265	+	4.51613i	0.622846	+	0.334758i
$183$	−14.3518			−1.06092
$184$	−2.64674	−	4.58428i	−0.195120	−	0.337958i
$185$	0.291713			0.0214471
$186$	3.24911	−	5.62762i	0.238236	−	0.412637i
$187$	5.56804	−	9.64413i	0.407176	−	0.705249i
$188$	0.976430	+	1.69123i	0.0712135	+	0.123345i
$189$	−2.45374	−	0.989520i	−0.178483	−	0.0719770i
$190$	4.18420			0.303554
$191$	−1.26373			−0.0914401			−0.0457200	−	0.998954i	$-0.514558\pi$
$191$	−1.26373			−0.0914401			−0.0457200	+	0.998954i	$0.514558\pi$
$192$	1.00000			0.0721688
$193$	18.9826			1.36640			0.683199	−	0.730232i	$-0.260588\pi$
$193$	18.9826			1.36640			0.683199	+	0.730232i	$0.260588\pi$
$194$	5.79259	−	10.0331i	0.415884	−	0.720332i
$195$	1.27919	+	2.91322i	0.0916048	+	0.208620i
$196$	−6.72632	+	1.93822i	−0.480451	+	0.138444i
$197$	12.1786	−	21.0939i	0.867688	−	1.50288i	0.00333546	−	0.999994i	$-0.498938\pi$
$197$	12.1786	−	21.0939i	0.867688	−	1.50288i	0.864353	−	0.502886i	$-0.167728\pi$
$198$	−0.775934	−	1.34396i	−0.0551433	−	0.0955109i
$199$	−10.7529	+	18.6246i	−0.762255	+	1.32026i	0.179430	+	0.983771i	$0.442575\pi$
$199$	−10.7529	+	18.6246i	−0.762255	+	1.32026i	−0.941686	+	0.336494i	$0.890759\pi$
$200$	2.11065	+	3.65575i	0.149245	+	0.258500i
$201$	−7.50473			−0.529343
$202$	−3.91439	−	6.77993i	−0.275416	−	0.477034i
$203$	−16.1494	+	12.6342i	−1.13346	+	0.886747i
$204$	3.58796	+	6.21453i	0.251207	+	0.435104i
$205$	−2.67308	−	4.62991i	−0.186696	−	0.323367i
$206$	−0.860345			−0.0599431
$207$	−2.64674	−	4.58428i	−0.183961	−	0.318630i
$208$	−3.58382	−	0.395262i	−0.248493	−	0.0274065i
$209$	7.35835			0.508988
$210$	−2.16529	−	0.873194i	−0.149419	−	0.0602561i
$211$	3.56775	−	6.17953i	0.245614	−	0.425416i	−0.716690	−	0.697392i	$-0.754344\pi$
$211$	3.56775	−	6.17953i	0.245614	−	0.425416i	0.962304	+	0.271976i	$0.0876771\pi$
$212$	13.4862			0.926233
$213$	5.00985	+	8.67732i	0.343270	+	0.594560i
$214$	4.07130	−	7.05170i	0.278308	−	0.482044i
$215$	−5.92958			−0.404394
$216$	1.00000			0.0680414
$217$	−2.40383	−	17.0238i	−0.163183	−	1.15565i
$218$	4.73806	−	8.20656i	0.320902	−	0.555818i
$219$	−1.93284	−	3.34778i	−0.130609	−	0.226222i
$220$	−0.684718	−	1.18597i	−0.0461637	−	0.0799578i
$221$	−10.4022	−	23.6899i	−0.699730	−	1.59356i
$222$	−0.165287	+	0.286285i	−0.0110933	+	0.0192142i
$223$	−12.1673	+	21.0744i	−0.814784	+	1.41125i	0.0946981	+	0.995506i	$0.469811\pi$
$223$	−12.1673	+	21.0744i	−0.814784	+	1.41125i	−0.909483	+	0.415742i	$0.863522\pi$
$224$	2.08382	−	1.63024i	0.139231	−	0.108925i
$225$	2.11065	+	3.65575i	0.140710	+	0.243717i
$226$	5.71537	−	9.89931i	0.380181	−	0.658492i
$227$	−4.78018	+	8.27951i	−0.317271	+	0.549530i	−0.979918	−	0.199402i	$-0.936100\pi$
$227$	−4.78018	+	8.27951i	−0.317271	+	0.549530i	0.662646	+	0.748933i	$0.269433\pi$
$228$	−2.37080	+	4.10635i	−0.157010	+	0.271950i
$229$	−5.40570	+	9.36295i	−0.357219	+	0.618721i	−0.987495	−	0.157650i	$-0.949608\pi$
$229$	−5.40570	+	9.36295i	−0.357219	+	0.618721i	0.630276	+	0.776371i	$0.282942\pi$
$230$	−2.33559	−	4.04537i	−0.154005	−	0.266744i
$231$	−3.80789	−	1.53560i	−0.250540	−	0.101035i
$232$	3.87494	−	6.71160i	0.254402	−	0.440638i
$233$	−5.15806	+	8.93403i	−0.337916	+	0.585288i	−0.984041	−	0.177944i	$-0.943055\pi$
$233$	−5.15806	+	8.93403i	−0.337916	+	0.585288i	0.646125	+	0.763232i	$0.276389\pi$
$234$	−3.58382	−	0.395262i	−0.234282	−	0.0258391i
$235$	0.861644	+	1.49241i	0.0562074	+	0.0973541i
$236$	−2.63569	−	4.56515i	−0.171569	−	0.297166i
$237$	6.67928	−	11.5689i	0.433866	−	0.751478i
$238$	17.6079	+	7.10071i	1.14135	+	0.460271i
$239$	11.0866			0.717130			0.358565	−	0.933505i	$-0.383266\pi$
$239$	11.0866			0.717130			0.358565	+	0.933505i	$0.383266\pi$
$240$	0.882443			0.0569614
$241$	9.33696	−	16.1721i	0.601447	−	1.04174i	−0.391156	−	0.920325i	$-0.627925\pi$
$241$	9.33696	−	16.1721i	0.601447	−	1.04174i	0.992602	−	0.121412i	$-0.0387421\pi$
$242$	4.29585	+	7.44063i	0.276148	+	0.478302i
$243$	1.00000			0.0641500
$244$	7.17592	−	12.4291i	0.459391	−	0.795689i
$245$	−5.93559	+	1.71036i	−0.379211	+	0.109271i
$246$	6.05836			0.386267
$247$	10.1196	−	13.7793i	0.643896	−	0.876758i
$248$	3.24911	+	5.62762i	0.206319	+	0.357354i
$249$	−10.5519			−0.668698
$250$	4.06863	+	7.04708i	0.257323	+	0.445696i
$251$	0.00354883	+	0.00614676i	0.000224000	+	0.000387980i	0.866137	−	0.499806i	$-0.166595\pi$
$251$	0.00354883	+	0.00614676i	0.000224000	+	0.000387980i	−0.865913	+	0.500194i	$0.833262\pi$
$252$	2.08382	−	1.63024i	0.131268	−	0.102696i
$253$	−4.10739	−	7.11421i	−0.258229	−	0.447266i
$254$	−6.05185			−0.379727
$255$	3.16617	+	5.48396i	0.198273	+	0.343419i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.33795	−	10.9776i	−0.395350	−	0.684767i	0.597795	−	0.801649i	$-0.296043\pi$
$257$	−6.33795	−	10.9776i	−0.395350	−	0.684767i	−0.993146	+	0.116882i	$0.962710\pi$
$258$	3.35975	−	5.81927i	0.209169	−	0.362292i
$259$	0.122287	+	0.866025i	0.00759852	+	0.0538122i
$260$	−3.16252	−	0.348796i	−0.196131	−	0.0216314i
$261$	3.87494	−	6.71160i	0.239853	−	0.415437i
$262$	5.32091			0.328727
$263$	−5.19802			−0.320523			−0.160262	−	0.987075i	$-0.551234\pi$
$263$	−5.19802			−0.320523			−0.160262	+	0.987075i	$0.551234\pi$
$264$	1.55187			0.0955109
$265$	11.9008			0.731058
$266$	1.75402	+	12.4219i	0.107546	+	0.761635i
$267$	−7.40837	−	12.8317i	−0.453385	−	0.785285i
$268$	3.75236	−	6.49929i	0.229212	−	0.397007i
$269$	0.342505	−	0.593235i	0.0208829	−	0.0361702i	−0.855395	−	0.517976i	$-0.826686\pi$
$269$	0.342505	−	0.593235i	0.0208829	−	0.0361702i	0.876278	+	0.481806i	$0.160019\pi$
$270$	0.882443			0.0537038
$271$	2.52563	+	4.37452i	0.153421	+	0.265733i	0.932483	−	0.361214i	$-0.117638\pi$
$271$	2.52563	+	4.37452i	0.153421	+	0.265733i	−0.779062	+	0.626947i	$0.784304\pi$
$272$	−7.17592			−0.435104
$273$	−8.11241	+	5.01884i	−0.490985	+	0.303754i
$274$	−8.01122			−0.483976
$275$	3.27545	+	5.67324i	0.197517	+	0.342109i
$276$	5.29348			0.318630
$277$	6.22484	−	10.7817i	0.374015	−	0.647812i	−0.616164	−	0.787618i	$-0.711314\pi$
$277$	6.22484	−	10.7817i	0.374015	−	0.647812i	0.990179	+	0.139805i	$0.0446477\pi$
$278$	8.87582	−	15.3734i	0.532337	−	0.922034i
$279$	3.24911	+	5.62762i	0.194519	+	0.336917i
$280$	1.83885	−	1.43860i	0.109892	−	0.0859726i
$281$	−23.5917			−1.40736			−0.703680	−	0.710517i	$-0.748461\pi$
$281$	−23.5917			−1.40736			−0.703680	+	0.710517i	$0.748461\pi$
$282$	−1.95286			−0.116291
$283$	21.0295			1.25008			0.625038	−	0.780594i	$-0.285083\pi$
$283$	21.0295			1.25008			0.625038	+	0.780594i	$0.285083\pi$
$284$	−10.0197			−0.594560
$285$	−2.09210	+	3.62362i	−0.123925	+	0.214645i
$286$	−5.56162	−	0.613395i	−0.328865	−	0.0362708i
$287$	12.6245	−	9.87660i	0.745203	−	0.582997i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−17.2469	−	29.8725i	−1.01452	−	1.75721i
$290$	3.41942	−	5.92260i	0.200795	−	0.347787i
$291$	5.79259	+	10.0331i	0.339568	+	0.588149i
$292$	3.86568			0.226222
$293$	−6.41251	−	11.1068i	−0.374623	−	0.648865i	0.615648	−	0.788021i	$-0.288894\pi$
$293$	−6.41251	−	11.1068i	−0.374623	−	0.648865i	−0.990270	+	0.139156i	$0.955561\pi$
$294$	1.68461	−	6.79427i	0.0982487	−	0.396250i
$295$	−2.32584	−	4.02848i	−0.135416	−	0.234547i
$296$	−0.165287	−	0.286285i	−0.00960711	−	0.0166400i
$297$	1.55187			0.0900486
$298$	−8.66161	−	15.0024i	−0.501754	−	0.869063i
$299$	−18.9709	−	2.09231i	−1.09711	−	0.121001i
$300$	−4.22129			−0.243717
$301$	−2.48569	−	17.6035i	−0.143273	−	1.01465i
$302$	−1.40927	+	2.44093i	−0.0810944	+	0.140460i
$303$	7.82879			0.449752
$304$	−2.37080	−	4.10635i	−0.135975	−	0.235515i
$305$	6.33234	−	10.9679i	0.362589	−	0.628022i
$306$	−7.17592			−0.410220
$307$	−20.4988			−1.16993			−0.584963	−	0.811060i	$-0.698891\pi$
$307$	−20.4988			−1.16993			−0.584963	+	0.811060i	$0.698891\pi$
$308$	3.23382	−	2.52992i	0.184264	−	0.144156i
$309$	0.430172	−	0.745081i	0.0244717	−	0.0423862i
$310$	2.86715	+	4.96605i	0.162843	+	0.282053i
$311$	7.06023	+	12.2287i	0.400349	+	0.693425i	0.993768	−	0.111469i	$-0.0355556\pi$
$311$	7.06023	+	12.2287i	0.400349	+	0.693425i	−0.593419	+	0.804894i	$0.702222\pi$
$312$	2.13422	−	2.90605i	0.120826	−	0.164523i
$313$	14.5296	−	25.1661i	0.821264	−	1.42247i	−0.0834772	−	0.996510i	$-0.526603\pi$
$313$	14.5296	−	25.1661i	0.821264	−	1.42247i	0.904741	−	0.425961i	$-0.140064\pi$
$314$	6.39822	−	11.0820i	0.361072	−	0.625396i
$315$	1.83885	−	1.43860i	0.103608	−	0.0810557i
$316$	6.67928	+	11.5689i	0.375739	+	0.650799i
$317$	−6.08027	+	10.5313i	−0.341502	+	0.591499i	−0.984712	−	0.174191i	$-0.944269\pi$
$317$	−6.08027	+	10.5313i	−0.341502	+	0.591499i	0.643210	+	0.765690i	$0.277602\pi$
$318$	−6.74308	+	11.6794i	−0.378133	+	0.654946i
$319$	6.01340	−	10.4155i	0.336686	−	0.583157i
$320$	−0.441221	+	0.764218i	−0.0246650	+	0.0427211i
$321$	4.07130	+	7.05170i	0.227238	+	0.393587i
$322$	11.0307	−	8.62965i	0.614714	−	0.480912i
$323$	17.0127	−	29.4669i	0.946612	−	1.63958i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	15.1284	+	1.66852i	0.839171	+	0.0925527i
$326$	5.34387	+	9.25586i	0.295970	+	0.512635i
$327$	4.73806	+	8.20656i	0.262015	+	0.453824i
$328$	−3.02918	+	5.24669i	−0.167259	+	0.289700i
$329$	−4.06941	+	3.18364i	−0.224354	+	0.175520i
$330$	1.36944			0.0753849
$331$	9.93371			0.546006			0.273003	−	0.962013i	$-0.411983\pi$
$331$	9.93371			0.546006			0.273003	+	0.962013i	$0.411983\pi$
$332$	5.27593	−	9.13819i	0.289555	−	0.501523i
$333$	−0.165287	−	0.286285i	−0.00905767	−	0.0156883i
$334$	19.8082			1.08386
$335$	3.31125	−	5.73525i	0.180913	−	0.313350i
$336$	0.369922	+	2.61976i	0.0201809	+	0.142920i
$337$	−3.38360			−0.184316			−0.0921582	−	0.995744i	$-0.529377\pi$
$337$	−3.38360			−0.184316			−0.0921582	+	0.995744i	$0.529377\pi$
$338$	−8.79730	+	9.57118i	−0.478510	+	0.520604i
$339$	5.71537	+	9.89931i	0.310416	+	0.537657i
$340$	−6.33234			−0.343419
$341$	5.04219	+	8.73333i	0.273050	+	0.472936i
$342$	−2.37080	−	4.10635i	−0.128198	−	0.222046i
$343$	−7.56588	−	16.9044i	−0.408519	−	0.912750i
$344$	3.35975	+	5.81927i	0.181146	+	0.313754i
$345$	4.67119			0.251488
$346$	0.869332	+	1.50573i	0.0467356	+	0.0809484i
$347$	−11.1272	+	19.2729i	−0.597340	+	1.03462i	0.395873	+	0.918305i	$0.370442\pi$
$347$	−11.1272	+	19.2729i	−0.597340	+	1.03462i	−0.993212	+	0.116317i	$0.962891\pi$
$348$	3.87494	+	6.71160i	0.207719	+	0.359779i
$349$	−5.16027	+	8.93784i	−0.276223	+	0.478432i	−0.970443	−	0.241331i	$-0.922416\pi$
$349$	−5.16027	+	8.93784i	−0.276223	+	0.478432i	0.694220	+	0.719763i	$0.255749\pi$
$350$	−8.79642	+	6.88174i	−0.470188	+	0.367844i
$351$	2.13422	−	2.90605i	0.113916	−	0.155113i
$352$	−0.775934	+	1.34396i	−0.0413574	+	0.0716332i
$353$	−0.970207			−0.0516389			−0.0258195	−	0.999667i	$-0.508220\pi$
$353$	−0.970207			−0.0516389			−0.0258195	+	0.999667i	$0.508220\pi$
$354$	5.27138			0.280171
$355$	−8.84182			−0.469275
$356$	14.8167			0.785285
$357$	−14.9533	+	11.6985i	−0.791414	+	0.619150i
$358$	−4.89644	−	8.48088i	−0.258785	−	0.448228i
$359$	−1.03017	+	1.78430i	−0.0543701	+	0.0941717i	−0.891929	−	0.452175i	$-0.850648\pi$
$359$	−1.03017	+	1.78430i	−0.0543701	+	0.0941717i	0.837559	+	0.546346i	$0.183982\pi$
$360$	−0.441221	+	0.764218i	−0.0232544	+	0.0402778i
$361$	3.48284			0.183307
$362$	5.79505	+	10.0373i	0.304581	+	0.527550i
$363$	−8.59170			−0.450947
$364$	−0.290241	−	9.53498i	−0.0152127	−	0.499769i
$365$	3.41124			0.178552
$366$	7.17592	+	12.4291i	0.375091	+	0.649677i
$367$	−9.27075			−0.483929			−0.241965	−	0.970285i	$-0.577792\pi$
$367$	−9.27075			−0.483929			−0.241965	+	0.970285i	$0.577792\pi$
$368$	−2.64674	+	4.58428i	−0.137971	+	0.238972i
$369$	−3.02918	+	5.24669i	−0.157693	+	0.273132i
$370$	−0.145856	−	0.252631i	−0.00758271	−	0.0131336i
$371$	4.98883	+	35.3305i	0.259007	+	1.83427i
$372$	−6.49821			−0.336917
$373$	−7.53237			−0.390011			−0.195006	−	0.980802i	$-0.562473\pi$
$373$	−7.53237			−0.390011			−0.195006	+	0.980802i	$0.562473\pi$
$374$	−11.1361			−0.575833
$375$	−8.13726			−0.420207
$376$	0.976430	−	1.69123i	0.0503555	−	0.0872184i
$377$	−11.2343	−	25.5848i	−0.578594	−	1.31768i
$378$	0.369922	+	2.61976i	0.0190267	+	0.134746i
$379$	−8.94169	+	15.4875i	−0.459304	+	0.795537i	−0.998924	−	0.0463711i	$-0.985234\pi$
$379$	−8.94169	+	15.4875i	−0.459304	+	0.795537i	0.539621	+	0.841908i	$0.318568\pi$
$380$	−2.09210	−	3.62362i	−0.107322	−	0.185888i
$381$	3.02592	−	5.24105i	0.155023	−	0.268507i
$382$	0.631864	+	1.09442i	0.0323290	+	0.0559954i
$383$	−18.1907			−0.929502			−0.464751	−	0.885441i	$-0.653856\pi$
$383$	−18.1907			−0.929502			−0.464751	+	0.885441i	$0.653856\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	2.85366	−	2.23251i	0.145436	−	0.113779i
$386$	−9.49130	−	16.4394i	−0.483095	−	0.836745i
$387$	3.35975	+	5.81927i	0.170786	+	0.295810i
$388$	−11.5852			−0.588149
$389$	8.54918	+	14.8076i	0.433461	+	0.750776i	0.997169	−	0.0751984i	$-0.0239590\pi$
$389$	8.54918	+	14.8076i	0.433461	+	0.750776i	−0.563708	+	0.825974i	$0.690626\pi$
$390$	1.88332	−	2.56442i	0.0953658	−	0.129855i
$391$	−37.9856			−1.92101
$392$	5.04170	+	4.85605i	0.254644	+	0.245268i
$393$	−2.66045	+	4.60804i	−0.134202	+	0.232445i
$394$	−24.3572			−1.22710
$395$	5.89408	+	10.2088i	0.296563	+	0.513663i
$396$	−0.775934	+	1.34396i	−0.0389922	+	0.0675364i
$397$	27.6771			1.38907			0.694536	−	0.719458i	$-0.255610\pi$
$397$	27.6771			1.38907			0.694536	+	0.719458i	$0.255610\pi$
$398$	21.5059			1.07799
$399$	−11.6347	−	4.69191i	−0.582463	−	0.234889i
$400$	2.11065	−	3.65575i	0.105532	−	0.182787i
$401$	0.392020	+	0.678998i	0.0195765	+	0.0339075i	0.875648	−	0.482950i	$-0.160435\pi$
$401$	0.392020	+	0.678998i	0.0195765	+	0.0339075i	−0.856071	+	0.516858i	$0.827102\pi$
$402$	3.75236	+	6.49929i	0.187151	+	0.324155i
$403$	23.2884	+	2.56850i	1.16008	+	0.127946i
$404$	−3.91439	+	6.77993i	−0.194748	+	0.337314i
$405$	−0.441221	+	0.764218i	−0.0219245	+	0.0379743i
$406$	19.0162	+	7.66866i	0.943759	+	0.380589i
$407$	−0.256504	−	0.444277i	−0.0127144	−	0.0220220i
$408$	3.58796	−	6.21453i	0.177630	−	0.307665i
$409$	−12.9870	+	22.4941i	−0.642164	+	1.11226i	0.342785	+	0.939414i	$0.388630\pi$
$409$	−12.9870	+	22.4941i	−0.642164	+	1.11226i	−0.984949	+	0.172846i	$0.944704\pi$
$410$	−2.67308	+	4.62991i	−0.132014	+	0.228655i
$411$	4.00561	−	6.93792i	0.197582	−	0.342222i
$412$	0.430172	+	0.745081i	0.0211931	+	0.0367075i
$413$	10.9846	−	8.59363i	0.540517	−	0.422865i
$414$	−2.64674	+	4.58428i	−0.130080	+	0.225305i
$415$	4.65571	−	8.06393i	0.228540	−	0.395843i
$416$	1.44960	+	3.30131i	0.0710726	+	0.161860i
$417$	8.87582	+	15.3734i	0.434651	+	0.752838i
$418$	−3.67918	−	6.37252i	−0.179954	−	0.311690i
$419$	0.207579	−	0.359537i	0.0101409	−	0.0175645i	−0.860910	−	0.508757i	$-0.830105\pi$
$419$	0.207579	−	0.359537i	0.0101409	−	0.0175645i	0.871051	+	0.491192i	$0.163439\pi$
$420$	0.326435	+	2.31179i	0.0159284	+	0.112804i
$421$	−8.45284			−0.411966			−0.205983	−	0.978556i	$-0.566039\pi$
$421$	−8.45284			−0.411966			−0.205983	+	0.978556i	$0.566039\pi$
$422$	−7.13550			−0.347351
$423$	0.976430	−	1.69123i	0.0474757	−	0.0822303i
$424$	−6.74308	−	11.6794i	−0.327473	−	0.567200i
$425$	30.2917			1.46936
$426$	5.00985	−	8.67732i	0.242728	−	0.420418i
$427$	35.2157	+	14.2014i	1.70421	+	0.687255i
$428$	−8.14260			−0.393587
$429$	3.31202	−	4.50981i	0.159906	−	0.217735i
$430$	2.96479	+	5.13517i	0.142975	+	0.247640i
$431$	−24.7870			−1.19395			−0.596973	−	0.802261i	$-0.703630\pi$
$431$	−24.7870			−1.19395			−0.596973	+	0.802261i	$0.703630\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	18.5723	+	32.1682i	0.892529	+	1.54591i	0.836833	+	0.547458i	$0.184405\pi$
$433$	18.5723	+	32.1682i	0.892529	+	1.54591i	0.0556964	+	0.998448i	$0.482262\pi$
$434$	−13.5411	+	10.5937i	−0.649994	+	0.508512i
$435$	3.41942	+	5.92260i	0.163948	+	0.283967i
$436$	−9.47612			−0.453824
$437$	−12.5498	−	21.7369i	−0.600338	−	1.03982i
$438$	−1.93284	+	3.34778i	−0.0923546	+	0.159963i
$439$	4.37683	+	7.58089i	0.208895	+	0.361816i	0.951367	−	0.308061i	$-0.0996800\pi$
$439$	4.37683	+	7.58089i	0.208895	+	0.361816i	−0.742472	+	0.669877i	$0.766347\pi$
$440$	−0.684718	+	1.18597i	−0.0326426	+	0.0565387i
$441$	5.04170	+	4.85605i	0.240081	+	0.231241i
$442$	−15.3150	+	20.8536i	−0.728459	+	0.991903i
$443$	1.48601	−	2.57384i	0.0706023	−	0.122287i	−0.828563	−	0.559896i	$-0.810841\pi$
$443$	1.48601	−	2.57384i	0.0706023	−	0.122287i	0.899165	+	0.437609i	$0.144175\pi$
$444$	0.330574			0.0156883
$445$	13.0749			0.619811
$446$	24.3347			1.15228
$447$	17.3232			0.819360
$448$	−2.45374	−	0.989520i	−0.115928	−	0.0467504i
$449$	2.95700	+	5.12167i	0.139549	+	0.241707i	0.927326	−	0.374254i	$-0.122101\pi$
$449$	2.95700	+	5.12167i	0.139549	+	0.241707i	−0.787777	+	0.615961i	$0.788768\pi$
$450$	2.11065	−	3.65575i	0.0994969	−	0.172334i
$451$	−4.70089	+	8.14218i	−0.221356	+	0.383400i
$452$	−11.4307			−0.537657
$453$	−1.40927	−	2.44093i	−0.0662133	−	0.114685i
$454$	9.56035			0.448690
$455$	−0.256121	−	8.41407i	−0.0120071	−	0.394458i
$456$	4.74161			0.222046
$457$	7.09665	+	12.2918i	0.331968	+	0.574985i	0.982898	−	0.184153i	$-0.0589542\pi$
$457$	7.09665	+	12.2918i	0.331968	+	0.574985i	−0.650930	+	0.759138i	$0.725621\pi$
$458$	10.8114			0.505183
$459$	3.58796	−	6.21453i	0.167472	−	0.290069i
$460$	−2.33559	+	4.04537i	−0.108898	+	0.188616i
$461$	15.1395	+	26.2224i	0.705117	+	1.22130i	0.966649	+	0.256104i	$0.0824391\pi$
$461$	15.1395	+	26.2224i	0.705117	+	1.22130i	−0.261532	+	0.965195i	$0.584228\pi$
$462$	0.574070	+	4.06553i	0.0267082	+	0.189145i
$463$	−32.8167			−1.52512			−0.762561	−	0.646916i	$-0.776059\pi$
$463$	−32.8167			−1.52512			−0.762561	+	0.646916i	$0.776059\pi$
$464$	−7.74989			−0.359779
$465$	−5.73430			−0.265922
$466$	10.3161			0.477885
$467$	−10.4247	+	18.0562i	−0.482399	+	0.835540i	−0.999796	−	0.0202058i	$-0.993568\pi$
$467$	−10.4247	+	18.0562i	−0.482399	+	0.835540i	0.517397	+	0.855746i	$0.326901\pi$
$468$	1.44960	+	3.30131i	0.0670079	+	0.152603i
$469$	18.4147	+	7.42608i	0.850310	+	0.342904i
$470$	0.861644	−	1.49241i	0.0397447	−	0.0688398i
$471$	6.39822	+	11.0820i	0.294814	+	0.510634i
$472$	−2.63569	+	4.56515i	−0.121317	+	0.210128i
$473$	5.21390	+	9.03074i	0.239735	+	0.415234i
$474$	−13.3586			−0.613579
$475$	10.0079	+	17.3341i	0.459192	+	0.795344i
$476$	−2.65453	−	18.7992i	−0.121670	−	0.861660i
$477$	−6.74308	−	11.6794i	−0.308744	−	0.534761i
$478$	−5.54328	−	9.60124i	−0.253544	−	0.439150i
$479$	−24.1901			−1.10527			−0.552637	−	0.833422i	$-0.686378\pi$
$479$	−24.1901			−1.10527			−0.552637	+	0.833422i	$0.686378\pi$
$480$	−0.441221	−	0.764218i	−0.0201389	−	0.0348816i
$481$	−1.18472	−	0.130663i	−0.0540185	−	0.00595774i
$482$	−18.6739			−0.850574
$483$	1.95817	+	13.8677i	0.0890999	+	0.631000i
$484$	4.29585	−	7.44063i	0.195266	−	0.338211i
$485$	−10.2233			−0.464215
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	20.1532	−	34.9064i	0.913230	−	1.58176i	0.103758	−	0.994603i	$-0.466913\pi$
$487$	20.1532	−	34.9064i	0.913230	−	1.58176i	0.809472	−	0.587158i	$-0.199753\pi$
$488$	−14.3518			−0.649677
$489$	−10.6877			−0.483317
$490$	4.44901	+	4.28519i	0.200986	+	0.193585i
$491$	−3.58602	+	6.21117i	−0.161835	+	0.280306i	−0.935527	−	0.353256i	$-0.885075\pi$
$491$	−3.58602	+	6.21117i	−0.161835	+	0.280306i	0.773692	+	0.633562i	$0.218408\pi$
$492$	−3.02918	−	5.24669i	−0.136566	−	0.236539i
$493$	−27.8063	−	48.1619i	−1.25233	−	2.16910i
$494$	−16.9931	−	1.87418i	−0.764554	−	0.0843232i
$495$	−0.684718	+	1.18597i	−0.0307758	+	0.0533052i
$496$	3.24911	−	5.62762i	0.145889	−	0.252688i
$497$	−3.70651	−	26.2493i	−0.166260	−	1.17744i
$498$	5.27593	+	9.13819i	0.236420	+	0.409492i
$499$	8.24802	−	14.2860i	0.369232	−	0.639528i	−0.620214	−	0.784433i	$-0.712954\pi$
$499$	8.24802	−	14.2860i	0.369232	−	0.639528i	0.989446	+	0.144904i	$0.0462875\pi$
$500$	4.06863	−	7.04708i	0.181955	−	0.315155i
$501$	−9.90412	+	17.1544i	−0.442484	+	0.766404i
$502$	0.00354883	−	0.00614676i	0.000158392	−	0.000274343i
$503$	0.187093	+	0.324055i	0.00834208	+	0.0144489i	0.870166	−	0.492758i	$-0.164011\pi$
$503$	0.187093	+	0.324055i	0.00834208	+	0.0144489i	−0.861824	+	0.507207i	$0.830678\pi$
$504$	−2.45374	−	0.989520i	−0.109298	−	0.0440767i
$505$	−3.45423	+	5.98290i	−0.153711	+	0.266236i
$506$	−4.10739	+	7.11421i	−0.182596	+	0.316265i
$507$	−3.89023	−	12.4043i	−0.172771	−	0.550893i
$508$	3.02592	+	5.24105i	0.134254	+	0.232534i
$509$	−2.63449	−	4.56308i	−0.116772	−	0.202255i	0.801715	−	0.597707i	$-0.203921\pi$
$509$	−2.63449	−	4.56308i	−0.116772	−	0.202255i	−0.918487	+	0.395452i	$0.870588\pi$
$510$	3.16617	−	5.48396i	0.140200	−	0.242834i
$511$	1.43000	+	10.1272i	0.0632594	+	0.447999i
$512$	1.00000			0.0441942
$513$	4.74161			0.209347
$514$	−6.33795	+	10.9776i	−0.279555	+	0.484203i
$515$	0.379603	+	0.657491i	0.0167273	+	0.0289725i
$516$	−6.71951			−0.295810
$517$	1.51529	−	2.62456i	0.0666424	−	0.115428i
$518$	0.688857	−	0.538916i	0.0302666	−	0.0236786i
$519$	−1.73866			−0.0763189
$520$	1.27919	+	2.91322i	0.0560963	+	0.127753i
$521$	3.43343	+	5.94687i	0.150421	+	0.260537i	0.931382	−	0.364042i	$-0.118604\pi$
$521$	3.43343	+	5.94687i	0.150421	+	0.260537i	−0.780961	+	0.624580i	$0.785270\pi$
$522$	−7.74989			−0.339203
$523$	1.09222	+	1.89179i	0.0477596	+	0.0827221i	0.888917	−	0.458068i	$-0.151459\pi$
$523$	1.09222	+	1.89179i	0.0477596	+	0.0827221i	−0.841157	+	0.540790i	$0.818125\pi$
$524$	−2.66045	−	4.60804i	−0.116222	−	0.201303i
$525$	−1.56155	−	11.0588i	−0.0681516	−	0.482645i
$526$	2.59901	+	4.50161i	0.113322	+	0.196280i
$527$	46.6307			2.03126
$528$	−0.775934	−	1.34396i	−0.0337682	−	0.0584883i
$529$	−2.51044	+	4.34822i	−0.109150	+	0.189053i
$530$	−5.95038	−	10.3064i	−0.258468	−	0.447680i
$531$	−2.63569	+	4.56515i	−0.114379	+	0.198111i
$532$	9.88066	−	7.72997i	0.428381	−	0.335137i
$533$	8.78222	+	20.0005i	0.380400	+	0.866319i
$534$	−7.40837	+	12.8317i	−0.320591	+	0.555281i
$535$	−7.18538			−0.310651
$536$	−7.50473			−0.324155
$537$	9.79287			0.422594
$538$	−0.685009			−0.0295328
$539$	7.82406	+	7.53596i	0.337006	+	0.324597i
$540$	−0.441221	−	0.764218i	−0.0189871	−	0.0328867i
$541$	−18.7629	+	32.4982i	−0.806679	+	1.39721i	0.108473	+	0.994099i	$0.465404\pi$
$541$	−18.7629	+	32.4982i	−0.806679	+	1.39721i	−0.915152	+	0.403109i	$0.867929\pi$
$542$	2.52563	−	4.37452i	0.108485	−	0.187902i
$543$	−11.5901			−0.497379
$544$	3.58796	+	6.21453i	0.153832	+	0.266446i
$545$	−8.36213			−0.358194
$546$	8.40265	+	4.51613i	0.359600	+	0.193273i
$547$	26.8987			1.15011			0.575054	−	0.818116i	$-0.304981\pi$
$547$	26.8987			1.15011			0.575054	+	0.818116i	$0.304981\pi$
$548$	4.00561	+	6.93792i	0.171111	+	0.296373i
$549$	−14.3518			−0.612521
$550$	3.27545	−	5.67324i	0.139666	−	0.241908i
$551$	18.3735	−	31.8238i	0.782736	−	1.35574i
$552$	−2.64674	−	4.58428i	−0.112653	−	0.195120i
$553$	−27.8368	+	21.7777i	−1.18374	+	0.926082i
$554$	−12.4497			−0.528937
$555$	0.291713			0.0123825
$556$	−17.7516			−0.752838
$557$	3.16671			0.134178			0.0670889	−	0.997747i	$-0.478629\pi$
$557$	3.16671			0.134178			0.0670889	+	0.997747i	$0.478629\pi$
$558$	3.24911	−	5.62762i	0.137546	−	0.238236i
$559$	24.0815	+	2.65597i	1.01854	+	0.112335i
$560$	−2.16529	−	0.873194i	−0.0915001	−	0.0368992i
$561$	5.56804	−	9.64413i	0.235083	−	0.407176i
$562$	11.7958	+	20.4310i	0.497577	+	0.861829i
$563$	−15.4492	+	26.7588i	−0.651106	+	1.12775i	0.331749	+	0.943368i	$0.392361\pi$
$563$	−15.4492	+	26.7588i	−0.651106	+	1.12775i	−0.982855	+	0.184380i	$0.940972\pi$
$564$	0.976430	+	1.69123i	0.0411151	+	0.0712135i
$565$	−10.0870			−0.424362
$566$	−10.5148	−	18.2121i	−0.441969	−	0.765512i
$567$	−2.45374	−	0.989520i	−0.103047	−	0.0415559i
$568$	5.00985	+	8.67732i	0.210209	+	0.364092i
$569$	−5.89141	−	10.2042i	−0.246981	−	0.427784i	0.715706	−	0.698402i	$-0.246105\pi$
$569$	−5.89141	−	10.2042i	−0.246981	−	0.427784i	−0.962687	+	0.270618i	$0.912772\pi$
$570$	4.18420			0.175257
$571$	−11.9777	−	20.7459i	−0.501250	−	0.868190i	−0.999999	−	0.00144398i	$-0.999540\pi$
$571$	−11.9777	−	20.7459i	−0.501250	−	0.868190i	0.498749	−	0.866746i	$-0.333793\pi$
$572$	2.24959	+	5.12320i	0.0940602	+	0.214212i
$573$	−1.26373			−0.0527930
$574$	−14.8657	−	5.99487i	−0.620481	−	0.250221i
$575$	11.1727	−	19.3516i	0.465932	−	0.807018i
$576$	1.00000			0.0416667
$577$	−13.2068	−	22.8748i	−0.549805	−	0.952291i	−0.998287	−	0.0584990i	$-0.981369\pi$
$577$	−13.2068	−	22.8748i	−0.549805	−	0.952291i	0.448482	−	0.893792i	$-0.351965\pi$
$578$	−17.2469	+	29.8725i	−0.717377	+	1.24253i
$579$	18.9826			0.788890
$580$	−6.83883			−0.283967
$581$	25.8916	+	10.4413i	1.07416	+	0.433177i
$582$	5.79259	−	10.0331i	0.240111	−	0.415884i
$583$	−10.4644	−	18.1248i	−0.433390	−	0.750654i
$584$	−1.93284	−	3.34778i	−0.0799815	−	0.138532i
$585$	1.27919	+	2.91322i	0.0528881	+	0.120447i
$586$	−6.41251	+	11.1068i	−0.264898	+	0.458817i
$587$	15.3403	−	26.5702i	0.633162	−	1.09667i	−0.353739	−	0.935344i	$-0.615090\pi$
$587$	15.3403	−	26.5702i	0.633162	−	1.09667i	0.986901	−	0.161325i	$-0.0515767\pi$
$588$	−6.72632	+	1.93822i	−0.277389	+	0.0799307i
$589$	15.4060	+	26.6840i	0.634793	+	1.09949i
$590$	−2.32584	+	4.02848i	−0.0957535	+	0.165850i
$591$	12.1786	−	21.0939i	0.500960	−	0.867688i
$592$	−0.165287	+	0.286285i	−0.00679325	+	0.0117663i
$593$	6.14941	−	10.6511i	0.252526	−	0.437388i	−0.711695	−	0.702489i	$-0.752072\pi$
$593$	6.14941	−	10.6511i	0.252526	−	0.437388i	0.964221	+	0.265101i	$0.0854054\pi$
$594$	−0.775934	−	1.34396i	−0.0318370	−	0.0551433i
$595$	−2.34247	−	16.5892i	−0.0960319	−	0.680092i
$596$	−8.66161	+	15.0024i	−0.354793	+	0.614520i
$597$	−10.7529	+	18.6246i	−0.440088	+	0.762255i
$598$	7.67344	+	17.4754i	0.313790	+	0.714623i
$599$	−3.22732	−	5.58989i	−0.131865	−	0.228397i	0.792531	−	0.609832i	$-0.208763\pi$
$599$	−3.22732	−	5.58989i	−0.131865	−	0.228397i	−0.924395	+	0.381436i	$0.875430\pi$
$600$	2.11065	+	3.65575i	0.0861668	+	0.149245i
$601$	−1.05552	+	1.82822i	−0.0430556	+	0.0745745i	−0.886750	−	0.462249i	$-0.847043\pi$
$601$	−1.05552	+	1.82822i	−0.0430556	+	0.0745745i	0.843695	+	0.536824i	$0.180376\pi$
$602$	−14.0022	+	10.9544i	−0.570689	+	0.446469i
$603$	−7.50473			−0.305616
$604$	2.81854			0.114685
$605$	3.79084	−	6.56593i	0.154120	−	0.266943i
$606$	−3.91439	−	6.77993i	−0.159011	−	0.275416i
$607$	25.1657			1.02144			0.510722	−	0.859746i	$-0.329378\pi$
$607$	25.1657			1.02144			0.510722	+	0.859746i	$0.329378\pi$
$608$	−2.37080	+	4.10635i	−0.0961488	+	0.166535i
$609$	−16.1494	+	12.6342i	−0.654405	+	0.511964i
$610$	−12.6647			−0.512778
$611$	−2.83087	−	6.44700i	−0.114525	−	0.260818i
$612$	3.58796	+	6.21453i	0.145035	+	0.251207i
$613$	−25.4546			−1.02810			−0.514052	−	0.857759i	$-0.671856\pi$
$613$	−25.4546			−1.02810			−0.514052	+	0.857759i	$0.671856\pi$
$614$	10.2494	+	17.7525i	0.413631	+	0.716431i
$615$	−2.67308	−	4.62991i	−0.107789	−	0.186696i
$616$	−3.80789	−	1.53560i	−0.153424	−	0.0618713i
$617$	16.4252	+	28.4493i	0.661254	+	1.14532i	0.980287	+	0.197581i	$0.0633086\pi$
$617$	16.4252	+	28.4493i	0.661254	+	1.14532i	−0.319033	+	0.947744i	$0.603358\pi$
$618$	−0.860345			−0.0346081
$619$	0.180058	+	0.311869i	0.00723713	+	0.0125351i	0.869621	−	0.493719i	$-0.164363\pi$
$619$	0.180058	+	0.311869i	0.00723713	+	0.0125351i	−0.862384	+	0.506254i	$0.831030\pi$
$620$	2.86715	−	4.96605i	0.115148	−	0.199441i
$621$	−2.64674	−	4.58428i	−0.106210	−	0.183961i
$622$	7.06023	−	12.2287i	0.283089	−	0.490325i
$623$	5.48103	+	38.8163i	0.219593	+	1.55514i
$624$	−3.58382	−	0.395262i	−0.143468	−	0.0158231i
$625$	−6.96290	+	12.0601i	−0.278516	+	0.482404i
$626$	−29.0593			−1.16144
$627$	7.35835			0.293864
$628$	−12.7964			−0.510634
$629$	−2.37217			−0.0945847
$630$	−2.16529	−	0.873194i	−0.0862671	−	0.0347889i
$631$	−7.36478	−	12.7562i	−0.293187	−	0.507815i	0.681374	−	0.731935i	$-0.261383\pi$
$631$	−7.36478	−	12.7562i	−0.293187	−	0.507815i	−0.974562	+	0.224120i	$0.928049\pi$
$632$	6.67928	−	11.5689i	0.265687	−	0.460184i
$633$	3.56775	−	6.17953i	0.141805	−	0.245614i
$634$	12.1605			0.482957
$635$	2.67020	+	4.62493i	0.105964	+	0.183535i
$636$	13.4862			0.534761
$637$	24.8720	−	4.28756i	0.985465	−	0.169879i
$638$	−12.0268			−0.476146
$639$	5.00985	+	8.67732i	0.198187	+	0.343270i
$640$	0.882443			0.0348816
$641$	24.1684	−	41.8609i	0.954595	−	1.65341i	0.219303	−	0.975657i	$-0.429622\pi$
$641$	24.1684	−	41.8609i	0.954595	−	1.65341i	0.735292	−	0.677751i	$-0.237045\pi$
$642$	4.07130	−	7.05170i	0.160681	−	0.278308i
$643$	−0.0861739	−	0.149258i	−0.00339837	−	0.00588614i	0.864321	−	0.502940i	$-0.167748\pi$
$643$	−0.0861739	−	0.149258i	−0.00339837	−	0.00588614i	−0.867720	+	0.497054i	$0.834415\pi$
$644$	−12.9888	−	5.23800i	−0.511831	−	0.206406i
$645$	−5.92958			−0.233477
$646$	−34.0254			−1.33871
$647$	27.9364			1.09829			0.549147	−	0.835725i	$-0.314953\pi$
$647$	27.9364			1.09829			0.549147	+	0.835725i	$0.314953\pi$
$648$	1.00000			0.0392837
$649$	−4.09024	+	7.08451i	−0.160556	+	0.278091i
$650$	−6.11920	−	13.9358i	−0.240015	−	0.546607i
$651$	−2.40383	−	17.0238i	−0.0942136	−	0.667215i
$652$	5.34387	−	9.25586i	0.209282	−	0.362487i
$653$	20.9244	+	36.2422i	0.818836	+	1.41827i	0.906540	+	0.422120i	$0.138714\pi$
$653$	20.9244	+	36.2422i	0.818836	+	1.41827i	−0.0877036	+	0.996147i	$0.527953\pi$
$654$	4.73806	−	8.20656i	0.185273	−	0.320902i
$655$	−2.34770	−	4.06633i	−0.0917322	−	0.158885i
$656$	6.05836			0.236539
$657$	−1.93284	−	3.34778i	−0.0754073	−	0.130609i
$658$	4.79182	+	1.93239i	0.186804	+	0.0753326i
$659$	3.26341	+	5.65240i	0.127125	+	0.220186i	0.922561	−	0.385850i	$-0.126092\pi$
$659$	3.26341	+	5.65240i	0.127125	+	0.220186i	−0.795437	+	0.606036i	$0.792759\pi$
$660$	−0.684718	−	1.18597i	−0.0266526	−	0.0461637i
$661$	1.05265			0.0409434			0.0204717	−	0.999790i	$-0.493483\pi$
$661$	1.05265			0.0409434			0.0204717	+	0.999790i	$0.493483\pi$
$662$	−4.96685	−	8.60284i	−0.193042	−	0.334359i
$663$	−10.4022	−	23.6899i	−0.403989	−	0.920041i
$664$	−10.5519			−0.409492
$665$	8.71911	−	6.82126i	0.338113	−	0.264517i
$666$	−0.165287	+	0.286285i	−0.00640474	+	0.0110933i
$667$	−41.0238			−1.58845
$668$	−9.90412	−	17.1544i	−0.383202	−	0.663725i
$669$	−12.1673	+	21.0744i	−0.470416	+	0.814784i
$670$	−6.62249			−0.255849
$671$	−22.2722			−0.859808
$672$	2.08382	−	1.63024i	0.0803851	−	0.0628880i
$673$	−13.1957	+	22.8556i	−0.508655	+	0.881017i	0.491294	+	0.870994i	$0.336524\pi$
$673$	−13.1957	+	22.8556i	−0.508655	+	0.881017i	−0.999950	+	0.0100234i	$0.996809\pi$
$674$	1.69180	+	2.93028i	0.0651657	+	0.112870i
$675$	2.11065	+	3.65575i	0.0812389	+	0.140710i
$676$	12.6875	+	2.83310i	0.487982	+	0.108965i
$677$	−10.3481	+	17.9235i	−0.397711	+	0.688856i	−0.993443	−	0.114327i	$-0.963529\pi$
$677$	−10.3481	+	17.9235i	−0.397711	+	0.688856i	0.595732	+	0.803183i	$0.296862\pi$
$678$	5.71537	−	9.89931i	0.219497	−	0.380181i
$679$	−4.28562	−	30.3504i	−0.164467	−	1.16474i
$680$	3.16617	+	5.48396i	0.121417	+	0.210300i
$681$	−4.78018	+	8.27951i	−0.183177	+	0.317271i
$682$	5.04219	−	8.73333i	0.193075	−	0.334416i
$683$	18.4894	−	32.0246i	0.707477	−	1.22539i	−0.258313	−	0.966061i	$-0.583167\pi$
$683$	18.4894	−	32.0246i	0.707477	−	1.22539i	0.965790	−	0.259325i	$-0.0835000\pi$
$684$	−2.37080	+	4.10635i	−0.0906499	+	0.157010i
$685$	3.53472	+	6.12232i	0.135055	+	0.233922i
$686$	−10.8567	+	15.0044i	−0.414510	+	0.572872i
$687$	−5.40570	+	9.36295i	−0.206240	+	0.357219i
$688$	3.35975	−	5.81927i	0.128089	−	0.221857i
$689$	−48.3320	−	5.33057i	−1.84130	−	0.203078i
$690$	−2.33559	−	4.04537i	−0.0889146	−	0.154005i
$691$	−1.75604	−	3.04155i	−0.0668029	−	0.115706i	0.830689	−	0.556736i	$-0.187947\pi$
$691$	−1.75604	−	3.04155i	−0.0668029	−	0.115706i	−0.897492	+	0.441030i	$0.854613\pi$
$692$	0.869332	−	1.50573i	0.0330470	−	0.0572391i
$693$	−3.80789	−	1.53560i	−0.144650	−	0.0583328i
$694$	22.2544			0.844766
$695$	−15.6648			−0.594200
$696$	3.87494	−	6.71160i	0.146879	−	0.254402i
$697$	21.7372	+	37.6499i	0.823353	+	1.42609i
$698$	10.3205			0.390638
$699$	−5.15806	+	8.93403i	−0.195096	+	0.337916i
$700$	10.3580	+	4.17705i	0.391494	+	0.157878i
$701$	−9.53390			−0.360090			−0.180045	−	0.983658i	$-0.557624\pi$
$701$	−9.53390			−0.360090			−0.180045	+	0.983658i	$0.557624\pi$
$702$	−3.58382	−	0.395262i	−0.135263	−	0.0149182i
$703$	−0.783726	−	1.35745i	−0.0295588	−	0.0511973i
$704$	1.55187			0.0584883
$705$	0.861644	+	1.49241i	0.0324514	+	0.0562074i
$706$	0.485103	+	0.840224i	0.0182571	+	0.0316222i
$707$	−19.2098	−	7.74674i	−0.722460	−	0.291346i
$708$	−2.63569	−	4.56515i	−0.0990553	−	0.171569i
$709$	19.1276			0.718352			0.359176	−	0.933270i	$-0.383058\pi$
$709$	19.1276			0.718352			0.359176	+	0.933270i	$0.383058\pi$
$710$	4.42091	+	7.65724i	0.165914	+	0.287371i
$711$	6.67928	−	11.5689i	0.250493	−	0.433866i
$712$	−7.40837	−	12.8317i	−0.277640	−	0.480887i
$713$	17.1991	−	29.7897i	0.644110	−	1.11563i
$714$	17.6079	+	7.10071i	0.658957	+	0.265738i
$715$	1.98514	+	4.52093i	0.0742399	+	0.169073i
$716$	−4.89644	+	8.48088i	−0.182988	+	0.316945i
$717$	11.0866			0.414035
$718$	2.06033			0.0768909
$719$	−27.7674			−1.03555			−0.517775	−	0.855517i	$-0.673239\pi$
$719$	−27.7674			−1.03555			−0.517775	+	0.855517i	$0.673239\pi$
$720$	0.882443			0.0328867
$721$	−1.79280	+	1.40257i	−0.0667675	+	0.0522345i
$722$	−1.74142	−	3.01623i	−0.0648089	−	0.112252i
$723$	9.33696	−	16.1721i	0.347245	−	0.601447i
$724$	5.79505	−	10.0373i	0.215371	−	0.373034i
$725$	32.7146			1.21499
$726$	4.29585	+	7.44063i	0.159434	+	0.276148i
$727$	27.4082			1.01651			0.508257	−	0.861205i	$-0.330290\pi$
$727$	27.4082			1.01651			0.508257	+	0.861205i	$0.330290\pi$
$728$	−8.11241	+	5.01884i	−0.300666	+	0.186011i
$729$	1.00000			0.0370370
$730$	−1.70562	−	2.95422i	−0.0631278	−	0.109341i
$731$	48.2187			1.78343
$732$	7.17592	−	12.4291i	0.265230	−	0.459391i
$733$	9.70789	−	16.8146i	0.358569	−	0.621060i	−0.629153	−	0.777282i	$-0.716598\pi$
$733$	9.70789	−	16.8146i	0.358569	−	0.621060i	0.987722	+	0.156222i	$0.0499314\pi$
$734$	4.63538	+	8.02871i	0.171095	+	0.296345i
$735$	−5.93559	+	1.71036i	−0.218937	+	0.0630877i
$736$	5.29348			0.195120
$737$	−11.6464			−0.428999
$738$	6.05836			0.223011
$739$	15.1617			0.557731			0.278866	−	0.960330i	$-0.410042\pi$
$739$	15.1617			0.557731			0.278866	+	0.960330i	$0.410042\pi$
$740$	−0.145856	+	0.252631i	−0.00536178	+	0.00928688i
$741$	10.1196	−	13.7793i	0.371754	−	0.506197i
$742$	28.1027	−	21.9857i	1.03168	−	0.807121i
$743$	−5.85184	+	10.1357i	−0.214683	+	0.371842i	−0.953174	−	0.302421i	$-0.902205\pi$
$743$	−5.85184	+	10.1357i	−0.214683	+	0.371842i	0.738491	+	0.674263i	$0.235539\pi$
$744$	3.24911	+	5.62762i	0.119118	+	0.206319i
$745$	−7.64338	+	13.2387i	−0.280032	+	0.485029i
$746$	3.76618	+	6.52322i	0.137890	+	0.238832i
$747$	−10.5519			−0.386073
$748$	5.56804	+	9.64413i	0.203588	+	0.352624i
$749$	−3.01213	−	21.3317i	−0.110061	−	0.779443i
$750$	4.06863	+	7.04708i	0.148565	+	0.257323i
$751$	−18.3916	−	31.8552i	−0.671119	−	1.16241i	−0.977587	−	0.210531i	$-0.932481\pi$
$751$	−18.3916	−	31.8552i	−0.671119	−	1.16241i	0.306468	−	0.951881i	$-0.400853\pi$
$752$	−1.95286			−0.0712135
$753$	0.00354883	+	0.00614676i	0.000129327	+	0.000224000i
$754$	−16.5399	+	22.5215i	−0.602349	+	0.820186i
$755$	2.48720			0.0905185
$756$	2.08382	−	1.63024i	0.0757878	−	0.0592914i
$757$	0.469542	−	0.813271i	0.0170658	−	0.0295589i	−0.857366	−	0.514707i	$-0.827901\pi$
$757$	0.469542	−	0.813271i	0.0170658	−	0.0295589i	0.874432	+	0.485148i	$0.161234\pi$
$758$	17.8834			0.649553
$759$	−4.10739	−	7.11421i	−0.149089	−	0.258229i
$760$	−2.09210	+	3.62362i	−0.0758884	+	0.131443i
$761$	−5.67119			−0.205580			−0.102790	−	0.994703i	$-0.532777\pi$
$761$	−5.67119			−0.205580			−0.102790	+	0.994703i	$0.532777\pi$
$762$	−6.05185			−0.219235
$763$	−3.50542	−	24.8252i	−0.126905	−	0.898732i
$764$	0.631864	−	1.09442i	0.0228600	−	0.0395947i
$765$	3.16617	+	5.48396i	0.114473	+	0.198273i
$766$	9.09536	+	15.7536i	0.328629	+	0.569201i
$767$	7.64141	+	17.4025i	0.275915	+	0.628366i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	0.775934	−	1.34396i	0.0279809	−	0.0484644i	−0.851696	−	0.524036i	$-0.824426\pi$
$769$	0.775934	−	1.34396i	0.0279809	−	0.0484644i	0.879677	+	0.475572i	$0.157759\pi$
$770$	−3.36024	−	1.35508i	−0.121095	−	0.0488338i
$771$	−6.33795	−	10.9776i	−0.228256	−	0.395350i
$772$	−9.49130	+	16.4394i	−0.341600	+	0.591668i
$773$	14.6797	−	25.4261i	0.527994	−	0.914512i	−0.471474	−	0.881880i	$-0.656278\pi$
$773$	14.6797	−	25.4261i	0.527994	−	0.914512i	0.999467	−	0.0326318i	$-0.0103889\pi$
$774$	3.35975	−	5.81927i	0.120764	−	0.209169i
$775$	−13.7154	+	23.7558i	−0.492673	+	0.853335i
$776$	5.79259	+	10.0331i	0.207942	+	0.360166i
$777$	0.122287	+	0.866025i	0.00438701	+	0.0310685i
$778$	8.54918	−	14.8076i	0.306503	−	0.530879i
$779$	−14.3632	+	24.8778i	−0.514615	+	0.891338i
$780$	−3.16252	−	0.348796i	−0.113236	−	0.0124889i
$781$	7.77464	+	13.4661i	0.278198	+	0.481854i
$782$	18.9928	+	32.8965i	0.679180	+	1.17637i
$783$	3.87494	−	6.71160i	0.138479	−	0.239853i
$784$	1.68461	−	6.79427i	0.0601648	−	0.242652i
$785$	−11.2921			−0.403033
$786$	5.32091			0.189791
$787$	9.16319	−	15.8711i	0.326632	−	0.565744i	−0.655209	−	0.755448i	$-0.727419\pi$
$787$	9.16319	−	15.8711i	0.326632	−	0.565744i	0.981841	+	0.189704i	$0.0607528\pi$
$788$	12.1786	+	21.0939i	0.433844	+	0.751440i
$789$	−5.19802			−0.185054
$790$	5.89408	−	10.2088i	0.209702	−	0.363215i
$791$	−4.22848	−	29.9458i	−0.150347	−	1.06475i
$792$	1.55187			0.0551433
$793$	−30.6299	+	41.7071i	−1.08770	+	1.48106i
$794$	−13.8385	−	23.9691i	−0.491111	−	0.850630i
$795$	11.9008			0.422077
$796$	−10.7529	−	18.6246i	−0.381128	−	0.660132i
$797$	6.67504	+	11.5615i	0.236442	+	0.409529i	0.959691	−	0.281058i	$-0.0906854\pi$
$797$	6.67504	+	11.5615i	0.236442	+	0.409529i	−0.723249	+	0.690588i	$0.757352\pi$
$798$	1.75402	+	12.4219i	0.0620918	+	0.439730i
$799$	−7.00678	−	12.1361i	−0.247882	−	0.429345i
$800$	−4.22129			−0.149245
$801$	−7.40837	−	12.8317i	−0.261762	−	0.453385i
$802$	0.392020	−	0.678998i	0.0138427	−	0.0239763i
$803$	−2.99951	−	5.19531i	−0.105851	−	0.183338i
$804$	3.75236	−	6.49929i	0.132336	−	0.229212i
$805$	−11.4619	−	4.62223i	−0.403979	−	0.162912i
$806$	−9.41983	−	21.4526i	−0.331799	−	0.755636i
$807$	0.342505	−	0.593235i	0.0120567	−	0.0208829i
$808$	7.82879			0.275416
$809$	−32.3855			−1.13861			−0.569307	−	0.822125i	$-0.692789\pi$
$809$	−32.3855			−1.13861			−0.569307	+	0.822125i	$0.692789\pi$
$810$	0.882443			0.0310059
$811$	−11.1640			−0.392022			−0.196011	−	0.980602i	$-0.562799\pi$
$811$	−11.1640			−0.392022			−0.196011	+	0.980602i	$0.562799\pi$
$812$	−2.86685	−	20.3029i	−0.100607	−	0.712491i
$813$	2.52563	+	4.37452i	0.0885778	+	0.153421i
$814$	−0.256504	+	0.444277i	−0.00899045	+	0.0155719i
$815$	4.71566	−	8.16777i	0.165182	−	0.286104i
$816$	−7.17592			−0.251207
$817$	15.9306	+	27.5927i	0.557342	+	0.965345i
$818$	25.9739			0.908157
$819$	−8.11241	+	5.01884i	−0.283471	+	0.175373i
$820$	5.34616			0.186696
$821$	15.8513	+	27.4552i	0.553213	+	0.958193i	0.998040	+	0.0625767i	$0.0199318\pi$
$821$	15.8513	+	27.4552i	0.553213	+	0.958193i	−0.444827	+	0.895616i	$0.646735\pi$
$822$	−8.01122			−0.279423
$823$	−26.2501	+	45.4665i	−0.915022	+	1.58486i	−0.108152	+	0.994134i	$0.534493\pi$
$823$	−26.2501	+	45.4665i	−0.915022	+	1.58486i	−0.806870	+	0.590729i	$0.798840\pi$
$824$	0.430172	−	0.745081i	0.0149858	−	0.0259561i
$825$	3.27545	+	5.67324i	0.114036	+	0.197517i
$826$	−12.9346	−	5.21613i	−0.450052	−	0.181492i
$827$	33.4939			1.16470			0.582348	−	0.812939i	$-0.302134\pi$
$827$	33.4939			1.16470			0.582348	+	0.812939i	$0.302134\pi$
$828$	5.29348			0.183961
$829$	−38.1248			−1.32413			−0.662064	−	0.749447i	$-0.730319\pi$
$829$	−38.1248			−1.32413			−0.662064	+	0.749447i	$0.730319\pi$
$830$	−9.31142			−0.323204
$831$	6.22484	−	10.7817i	0.215937	−	0.374015i
$832$	2.13422	−	2.90605i	0.0739907	−	0.100749i
$833$	48.2675	−	13.9085i	1.67237	−	0.481900i
$834$	8.87582	−	15.3734i	0.307345	−	0.532337i
$835$	−8.73982	−	15.1378i	−0.302454	−	0.523866i
$836$	−3.67918	+	6.37252i	−0.127247	+	0.220398i
$837$	3.24911	+	5.62762i	0.112306	+	0.194519i
$838$	−0.415158			−0.0143414
$839$	12.6246	+	21.8665i	0.435851	+	0.754916i	0.997365	−	0.0725514i	$-0.0231141\pi$
$839$	12.6246	+	21.8665i	0.435851	+	0.754916i	−0.561514	+	0.827467i	$0.689781\pi$
$840$	1.83885	−	1.43860i	0.0634464	−	0.0496363i
$841$	−15.5304	−	26.8994i	−0.535530	−	0.927565i
$842$	4.22642	+	7.32037i	0.145652	+	0.252277i
$843$	−23.5917			−0.812540
$844$	3.56775	+	6.17953i	0.122807	+	0.212708i
$845$	11.1960	+	2.50005i	0.385155	+	0.0860042i
$846$	−1.95286			−0.0671407
$847$	21.0818	+	8.50166i	0.724380	+	0.292120i
$848$	−6.74308	+	11.6794i	−0.231558	+	0.401071i
$849$	21.0295			0.721732
$850$	−15.1458	−	26.2334i	−0.519498	−	0.899797i
$851$	−0.874943	+	1.51545i	−0.0299926	+	0.0519488i
$852$	−10.0197			−0.343270
$853$	30.1001			1.03061			0.515304	−	0.857007i	$-0.327679\pi$
$853$	30.1001			1.03061			0.515304	+	0.857007i	$0.327679\pi$
$854$	−5.30906	−	37.5984i	−0.181672	−	1.28659i
$855$	−2.09210	+	3.62362i	−0.0715483	+	0.123925i
$856$	4.07130	+	7.05170i	0.139154	+	0.241022i
$857$	−11.8157	−	20.4655i	−0.403618	−	0.699087i	0.590541	−	0.807007i	$-0.298914\pi$
$857$	−11.8157	−	20.4655i	−0.403618	−	0.699087i	−0.994160	+	0.107920i	$0.965581\pi$
$858$	−5.56162	−	0.613395i	−0.189871	−	0.0209410i
$859$	−17.7282	+	30.7061i	−0.604878	+	1.04768i	0.387193	+	0.921999i	$0.373445\pi$
$859$	−17.7282	+	30.7061i	−0.604878	+	1.04768i	−0.992071	+	0.125680i	$0.959889\pi$
$860$	2.96479	−	5.13517i	0.101099	−	0.175108i
$861$	12.6245	−	9.87660i	0.430243	−	0.336594i
$862$	12.3935	+	21.4662i	0.422124	+	0.731140i
$863$	0.0283138	−	0.0490410i	0.000963813	−	0.00166937i	−0.865543	−	0.500834i	$-0.833027\pi$
$863$	0.0283138	−	0.0490410i	0.000963813	−	0.00166937i	0.866507	+	0.499165i	$0.166360\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	0.767135	−	1.32872i	0.0260834	−	0.0451778i
$866$	18.5723	−	32.1682i	0.631114	−	1.09312i
$867$	−17.2469	−	29.8725i	−0.585736	−	1.01452i
$868$	15.9449	+	6.43011i	0.541207	+	0.218252i
$869$	10.3654	−	17.9533i	0.351621	−	0.609025i
$870$	3.41942	−	5.92260i	0.115929	−	0.200795i
$871$	−16.0167	+	21.8091i	−0.542706	+	0.738973i
$872$	4.73806	+	8.20656i	0.160451	+	0.277909i
$873$	5.79259	+	10.0331i	0.196050	+	0.339568i
$874$	−12.5498	+	21.7369i	−0.424503	+	0.735261i
$875$	19.9667	+	8.05198i	0.674999	+	0.272207i
$876$	3.86568			0.130609
$877$	34.0163			1.14865			0.574324	−	0.818628i	$-0.305265\pi$
$877$	34.0163			1.14865			0.574324	+	0.818628i	$0.305265\pi$
$878$	4.37683	−	7.58089i	0.147711	−	0.255843i
$879$	−6.41251	−	11.1068i	−0.216288	−	0.374623i
$880$	1.36944			0.0461637
$881$	19.0164	−	32.9374i	0.640680	−	1.10969i	−0.344601	−	0.938749i	$-0.611986\pi$
$881$	19.0164	−	32.9374i	0.640680	−	1.10969i	0.985281	−	0.170941i	$-0.0546807\pi$
$882$	1.68461	−	6.79427i	0.0567239	−	0.228775i
$883$	22.6536			0.762356			0.381178	−	0.924502i	$-0.375519\pi$
$883$	22.6536			0.762356			0.381178	+	0.924502i	$0.375519\pi$
$884$	25.7172	+	2.83637i	0.864963	+	0.0953974i
$885$	−2.32584	−	4.02848i	−0.0781824	−	0.135416i
$886$	−2.97201			−0.0998468
$887$	−10.6538	−	18.4530i	−0.357720	−	0.619590i	0.629859	−	0.776709i	$-0.283113\pi$
$887$	−10.6538	−	18.4530i	−0.357720	−	0.619590i	−0.987580	+	0.157120i	$0.949779\pi$
$888$	−0.165287	−	0.286285i	−0.00554667	−	0.00960711i
$889$	−12.6110	+	9.86598i	−0.422958	+	0.330894i
$890$	−6.53746	−	11.3232i	−0.219136	−	0.379555i
$891$	1.55187			0.0519896
$892$	−12.1673	−	21.0744i	−0.407392	−	0.705624i
$893$	4.62985	−	8.01913i	0.154932	−	0.268350i
$894$	−8.66161	−	15.0024i	−0.289688	−	0.501754i
$895$	−4.32082	+	7.48389i	−0.144429	+	0.250159i
$896$	0.369922	+	2.61976i	0.0123582	+	0.0875201i
$897$	−18.9709	−	2.09231i	−0.633419	−	0.0698602i
$898$	2.95700	−	5.12167i	0.0986764	−	0.170912i
$899$	50.3604			1.67961
$900$	−4.22129			−0.140710
$901$	−96.7756			−3.22406
$902$	9.40178			0.313045
$903$	−2.48569	−	17.6035i	−0.0827187	−	0.585809i
$904$	5.71537	+	9.89931i	0.190090	+	0.329246i
$905$	5.11380	−	8.85736i	0.169989	−	0.294429i
$906$	−1.40927	+	2.44093i	−0.0468199	+	0.0810944i
$907$	53.4044			1.77326			0.886632	−	0.462475i	$-0.153039\pi$
$907$	53.4044			1.77326			0.886632	+	0.462475i	$0.153039\pi$
$908$	−4.78018	−	8.27951i	−0.158636	−	0.274765i
$909$	7.82879			0.259665
$910$	−7.15874	+	4.42884i	−0.237310	+	0.146815i
$911$	5.96942			0.197776			0.0988878	−	0.995099i	$-0.468472\pi$
$911$	5.96942			0.197776			0.0988878	+	0.995099i	$0.468472\pi$
$912$	−2.37080	−	4.10635i	−0.0785052	−	0.135975i
$913$	−16.3751			−0.541937
$914$	7.09665	−	12.2918i	0.234736	−	0.406575i
$915$	6.33234	−	10.9679i	0.209341	−	0.362589i
$916$	−5.40570	−	9.36295i	−0.178609	−	0.309360i
$917$	11.0878	−	8.67437i	0.366152	−	0.286453i
$918$	−7.17592			−0.236841
$919$	−26.8406			−0.885389			−0.442695	−	0.896672i	$-0.645977\pi$
$919$	−26.8406			−0.885389			−0.442695	+	0.896672i	$0.645977\pi$
$920$	4.67119			0.154005
$921$	−20.4988			−0.675457
$922$	15.1395	−	26.2224i	0.498593	−	0.863589i
$923$	35.9088	+	3.96041i	1.18195	+	0.130358i
$924$	3.23382	−	2.52992i	0.106385	−	0.0832284i
$925$	0.697725	−	1.20850i	0.0229411	−	0.0397351i
$926$	16.4084	+	28.4201i	0.539212	+	0.933943i
$927$	0.430172	−	0.745081i	0.0141287	−	0.0244717i
$928$	3.87494	+	6.71160i	0.127201	+	0.220319i
$929$	−8.21322			−0.269467			−0.134734	−	0.990882i	$-0.543018\pi$
$929$	−8.21322			−0.269467			−0.134734	+	0.990882i	$0.543018\pi$
$930$	2.86715	+	4.96605i	0.0940176	+	0.162843i
$931$	23.9058	+	23.0255i	0.783480	+	0.754630i
$932$	−5.15806	−	8.93403i	−0.168958	−	0.292644i
$933$	7.06023	+	12.2287i	0.231142	+	0.400349i
$934$	20.8495			0.682215
$935$	4.91348	+	8.51039i	0.160688	+	0.278320i
$936$	2.13422	−	2.90605i	0.0697591	−	0.0949872i
$937$	−22.5249			−0.735855			−0.367927	−	0.929854i	$-0.619933\pi$
$937$	−22.5249			−0.735855			−0.367927	+	0.929854i	$0.619933\pi$
$938$	−2.77616	−	19.6606i	−0.0906450	−	0.641942i
$939$	14.5296	−	25.1661i	0.474157	−	0.821264i
$940$	−1.72329			−0.0562074
$941$	−7.98410	−	13.8289i	−0.260274	−	0.450808i	0.706040	−	0.708172i	$-0.250480\pi$
$941$	−7.98410	−	13.8289i	−0.260274	−	0.450808i	−0.966315	+	0.257363i	$0.917146\pi$
$942$	6.39822	−	11.0820i	0.208465	−	0.361072i
$943$	32.0698			1.04434
$944$	5.27138			0.171569
$945$	1.83885	−	1.43860i	0.0598179	−	0.0467975i
$946$	5.21390	−	9.03074i	0.169518	−	0.293615i
$947$	0.675037	+	1.16920i	0.0219358	+	0.0379938i	0.876785	−	0.480883i	$-0.159684\pi$
$947$	0.675037	+	1.16920i	0.0219358	+	0.0379938i	−0.854849	+	0.518877i	$0.826350\pi$
$948$	6.67928	+	11.5689i	0.216933	+	0.375739i
$949$	−13.8539	−	1.52796i	−0.449717	−	0.0495996i
$950$	10.0079	−	17.3341i	0.324698	−	0.562393i
$951$	−6.08027	+	10.5313i	−0.197166	+	0.341502i
$952$	−14.9533	+	11.6985i	−0.484640	+	0.379150i
$953$	−21.1684	−	36.6647i	−0.685711	−	1.18769i	−0.973213	−	0.229906i	$-0.926158\pi$
$953$	−21.1684	−	36.6647i	−0.685711	−	1.18769i	0.287502	−	0.957780i	$-0.407175\pi$
$954$	−6.74308	+	11.6794i	−0.218315	+	0.378133i
$955$	0.557583	−	0.965763i	0.0180430	−	0.0312513i
$956$	−5.54328	+	9.60124i	−0.179282	+	0.310526i
$957$	6.01340	−	10.4155i	0.194386	−	0.336686i
$958$	12.0950	+	20.9492i	0.390773	+	0.676839i
$959$	−16.6939	+	13.0602i	−0.539076	+	0.421737i
$960$	−0.441221	+	0.764218i	−0.0142404	+	0.0246650i
$961$	−5.61340	+	9.72269i	−0.181077	+	0.313635i
$962$	0.479201	+	1.09133i	0.0154501	+	0.0351858i
$963$	4.07130	+	7.05170i	0.131196	+	0.227238i
$964$	9.33696	+	16.1721i	0.300723	+	0.520868i
$965$	−8.37553	+	14.5068i	−0.269618	+	0.466992i
$966$	11.0307	−	8.62965i	0.354905	−	0.277655i
$967$	−24.2814			−0.780838			−0.390419	−	0.920637i	$-0.627670\pi$
$967$	−24.2814			−0.780838			−0.390419	+	0.920637i	$0.627670\pi$
$968$	−8.59170			−0.276148
$969$	17.0127	−	29.4669i	0.546526	−	0.946612i
$970$	5.11163	+	8.85361i	0.164125	+	0.284272i
$971$	−24.7384			−0.793892			−0.396946	−	0.917842i	$-0.629930\pi$
$971$	−24.7384			−0.793892			−0.396946	+	0.917842i	$0.629930\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−6.56672	−	46.5051i	−0.210519	−	1.49089i
$974$	−40.3065			−1.29150
$975$	15.1284	+	1.66852i	0.484495	+	0.0534353i
$976$	7.17592	+	12.4291i	0.229696	+	0.397844i
$977$	−5.67559			−0.181578			−0.0907892	−	0.995870i	$-0.528939\pi$
$977$	−5.67559			−0.181578			−0.0907892	+	0.995870i	$0.528939\pi$
$978$	5.34387	+	9.25586i	0.170878	+	0.295970i
$979$	−11.4968	−	19.9131i	−0.367440	−	0.636424i
$980$	1.48658	−	5.99555i	0.0474869	−	0.191521i
$981$	4.73806	+	8.20656i	0.151275	+	0.262015i
$982$	7.17205			0.228869
$983$	−14.6863	−	25.4374i	−0.468419	−	0.811326i	0.530929	−	0.847416i	$-0.321843\pi$
$983$	−14.6863	−	25.4374i	−0.468419	−	0.811326i	−0.999349	+	0.0360900i	$0.988510\pi$
$984$	−3.02918	+	5.24669i	−0.0965668	+	0.167259i
$985$	10.7469	+	18.6142i	0.342425	+	0.593097i
$986$	−27.8063	+	48.1619i	−0.885532	+	1.53379i
$987$	−4.06941	+	3.18364i	−0.129531	+	0.101336i
$988$	6.87345	+	15.6535i	0.218674	+	0.498005i
$989$	17.7848	−	30.8041i	0.565523	−	0.979515i
$990$	1.36944			0.0435235
$991$	5.60608			0.178083			0.0890414	−	0.996028i	$-0.471620\pi$
$991$	5.60608			0.178083			0.0890414	+	0.996028i	$0.471620\pi$
$992$	−6.49821			−0.206319
$993$	9.93371			0.315237
$994$	−20.8793	+	16.3346i	−0.662250	+	0.518101i
$995$	−9.48885	−	16.4352i	−0.300817	−	0.521030i
$996$	5.27593	−	9.13819i	0.167174	−	0.289555i
$997$	−26.0345	+	45.0930i	−0.824520	+	1.42811i	0.0777663	+	0.996972i	$0.475221\pi$
$997$	−26.0345	+	45.0930i	−0.824520	+	1.42811i	−0.902286	+	0.431138i	$0.858112\pi$
$998$	−16.4960			−0.522173
$999$	−0.165287	−	0.286285i	−0.00522945	−	0.00905767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.k.c.373.2	yes	8
3.2	odd	2		1638.2.p.h.919.3		8
7.4	even	3		546.2.j.c.529.2	yes	8
13.3	even	3		546.2.j.c.289.2	✓	8
21.11	odd	6		1638.2.m.h.1621.3		8
39.29	odd	6		1638.2.m.h.289.3		8
91.81	even	3	inner	546.2.k.c.445.2	yes	8
273.263	odd	6		1638.2.p.h.991.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.c.289.2	✓	8	13.3	even	3
546.2.j.c.529.2	yes	8	7.4	even	3
546.2.k.c.373.2	yes	8	1.1	even	1	trivial
546.2.k.c.445.2	yes	8	91.81	even	3	inner
1638.2.m.h.289.3		8	39.29	odd	6
1638.2.m.h.1621.3		8	21.11	odd	6
1638.2.p.h.919.3		8	3.2	odd	2
1638.2.p.h.991.3		8	273.263	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.441221 + 0.764218i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.45374 - 0.989520i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.441221 + 0.764218i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.45374 - 0.989520i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.882443 q^{10} +1.55187 q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.13422 - 2.90605i) q^{13} +(0.369922 + 2.61976i) q^{14} +(-0.441221 + 0.764218i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.58796 - 6.21453i) q^{17} +(-0.500000 - 0.866025i) q^{18} +4.74161 q^{19} +(-0.441221 - 0.764218i) q^{20} +(-2.45374 - 0.989520i) q^{21} +(-0.775934 - 1.34396i) q^{22} +(-2.64674 - 4.58428i) q^{23} +1.00000 q^{24} +(2.11065 + 3.65575i) q^{25} +(-3.58382 - 0.395262i) q^{26} +1.00000 q^{27} +(2.08382 - 1.63024i) q^{28} +(3.87494 - 6.71160i) q^{29} +0.882443 q^{30} +(3.24911 + 5.62762i) q^{31} +(-0.500000 + 0.866025i) q^{32} +1.55187 q^{33} -7.17592 q^{34} +(1.83885 - 1.43860i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.165287 - 0.286285i) q^{37} +(-2.37080 - 4.10635i) q^{38} +(2.13422 - 2.90605i) q^{39} +(-0.441221 + 0.764218i) q^{40} +(-3.02918 + 5.24669i) q^{41} +(0.369922 + 2.61976i) q^{42} +(3.35975 + 5.81927i) q^{43} +(-0.775934 + 1.34396i) q^{44} +(-0.441221 + 0.764218i) q^{45} +(-2.64674 + 4.58428i) q^{46} +(0.976430 - 1.69123i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(5.04170 + 4.85605i) q^{49} +(2.11065 - 3.65575i) q^{50} +(3.58796 - 6.21453i) q^{51} +(1.44960 + 3.30131i) q^{52} +(-6.74308 - 11.6794i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.684718 + 1.18597i) q^{55} +(-2.45374 - 0.989520i) q^{56} +4.74161 q^{57} -7.74989 q^{58} +(-2.63569 + 4.56515i) q^{59} +(-0.441221 - 0.764218i) q^{60} -14.3518 q^{61} +(3.24911 - 5.62762i) q^{62} +(-2.45374 - 0.989520i) q^{63} +1.00000 q^{64} +(1.27919 + 2.91322i) q^{65} +(-0.775934 - 1.34396i) q^{66} -7.50473 q^{67} +(3.58796 + 6.21453i) q^{68} +(-2.64674 - 4.58428i) q^{69} +(-2.16529 - 0.873194i) q^{70} +(5.00985 + 8.67732i) q^{71} +1.00000 q^{72} +(-1.93284 - 3.34778i) q^{73} +(-0.165287 + 0.286285i) q^{74} +(2.11065 + 3.65575i) q^{75} +(-2.37080 + 4.10635i) q^{76} +(-3.80789 - 1.53560i) q^{77} +(-3.58382 - 0.395262i) q^{78} +(6.67928 - 11.5689i) q^{79} +0.882443 q^{80} +1.00000 q^{81} +6.05836 q^{82} -10.5519 q^{83} +(2.08382 - 1.63024i) q^{84} +(3.16617 + 5.48396i) q^{85} +(3.35975 - 5.81927i) q^{86} +(3.87494 - 6.71160i) q^{87} +1.55187 q^{88} +(-7.40837 - 12.8317i) q^{89} +0.882443 q^{90} +(-8.11241 + 5.01884i) q^{91} +5.29348 q^{92} +(3.24911 + 5.62762i) q^{93} -1.95286 q^{94} +(-2.09210 + 3.62362i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(5.79259 + 10.0331i) q^{97} +(1.68461 - 6.79427i) q^{98} +1.55187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 2 q^{5} - 4 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 2 * q^5 - 4 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 2 q^{5} - 4 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} + 4 q^{23} + 8 q^{24} + 2 q^{25} - 12 q^{26} + 8 q^{27} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 4 q^{32} - 8 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} - 6 q^{37} - 4 q^{38} + 3 q^{39} + 2 q^{40} + 12 q^{41} + 3 q^{42} + 4 q^{44} + 2 q^{45} + 4 q^{46} + 7 q^{47} - 4 q^{48} - 7 q^{49} + 2 q^{50} - 2 q^{51} + 9 q^{52} - q^{53} - 4 q^{54} - 25 q^{55} - 3 q^{56} + 8 q^{57} - 4 q^{58} + 16 q^{59} + 2 q^{60} + 8 q^{61} + 14 q^{62} - 3 q^{63} + 8 q^{64} + q^{65} + 4 q^{66} - 38 q^{67} - 2 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} + 8 q^{72} - 7 q^{73} - 6 q^{74} + 2 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} - 4 q^{80} + 8 q^{81} - 24 q^{82} - 64 q^{83} + 15 q^{85} + 2 q^{87} - 8 q^{88} - 11 q^{89} - 4 q^{90} - 20 q^{91} - 8 q^{92} + 14 q^{93} - 14 q^{94} + 28 q^{95} - 4 q^{96} + 11 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 2 * q^5 - 4 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 4 * q^10 - 8 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 + 2 * q^15 - 4 * q^16 - 2 * q^17 - 4 * q^18 + 8 * q^19 + 2 * q^20 - 3 * q^21 + 4 * q^22 + 4 * q^23 + 8 * q^24 + 2 * q^25 - 12 * q^26 + 8 * q^27 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 4 * q^32 - 8 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 - 6 * q^37 - 4 * q^38 + 3 * q^39 + 2 * q^40 + 12 * q^41 + 3 * q^42 + 4 * q^44 + 2 * q^45 + 4 * q^46 + 7 * q^47 - 4 * q^48 - 7 * q^49 + 2 * q^50 - 2 * q^51 + 9 * q^52 - q^53 - 4 * q^54 - 25 * q^55 - 3 * q^56 + 8 * q^57 - 4 * q^58 + 16 * q^59 + 2 * q^60 + 8 * q^61 + 14 * q^62 - 3 * q^63 + 8 * q^64 + q^65 + 4 * q^66 - 38 * q^67 - 2 * q^68 + 4 * q^69 - 22 * q^70 + 20 * q^71 + 8 * q^72 - 7 * q^73 - 6 * q^74 + 2 * q^75 - 4 * q^76 - 24 * q^77 - 12 * q^78 + 24 * q^79 - 4 * q^80 + 8 * q^81 - 24 * q^82 - 64 * q^83 + 15 * q^85 + 2 * q^87 - 8 * q^88 - 11 * q^89 - 4 * q^90 - 20 * q^91 - 8 * q^92 + 14 * q^93 - 14 * q^94 + 28 * q^95 - 4 * q^96 + 11 * q^97 + 2 * q^98 - 8 * q^99

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